So, I think I've seen you post about this before (apologies if not!) but the amount of "Mahidevran doomed her son by making him think he had a right to the throne over others/was above his father" comments I keep seeing are starting to feel a little wild when I can count any examples of this on one hand (and many of them were fairly innocent, like her interaction with him in the first episode).
I don't recall posting about this in particular (though I did ask here a few months ago when did Mahidevran lie directly to Mustafa except for the three times in E48, because I have seen so many people talk about her lying to him as if it's something she frequently does. If there truly aren't any other cases of this, here's yet another statement blown out of proportion.), but it must be something mostly from the YT comments again, right? Ooof, they drive me crazy. It's not as simple as that.
Mustafa becoming the padişah truly is a belief Mahidevran held throughout the series. Every mother of a heir would believe or would want to believe that in such a system and it was especially understandable when Mahidevran believed that at first - she seemed to enter in an entirely new, advantageous environment where Süleiman became a padişah and Mustafa was the only heir to his throne. The kid certainly had the same expectations his mother gave him in their conversations before their arrival, that it's their castle and everyone would be waiting for them. But these expectations didn't necessarily amount to him being the next padişah or the special hair - what Mustafa was especially distraught at was the fact that he couldn't see his father or Ibrahim, like he apparently so often did in Manisa. Mustafa's motivations were always more familial in nature for the entirely of MC: here, as a little kid, he wanted his father to spend time with him, to play with him, to be next to him everywhere, as seen by his constant innocent child desires to go to a campaign with him and the little shot where he watched him during the divan in E02. It's this what made him raise his voice and try to assert himself. And for what is worth, Mahidevran also tried to ease him into the new circumstances, as much as she herself was struggling to - telling him that his father and/or Ibrahim had work and he couldn't see them at that moment. (also trying to calm him down when he was asking why doesn't his father come anymore, but that's besides the point here.) That wasn't her always telling him he has a special right over everyone, she realizes what's going on in the present despite of all and doesn't always latch onto her beliefs. Mustafa had an "independent spirit" right from the very beginning and there were instances where he didn't listen to his mother, even before he grew up - like him refusing to go to school. He always had firm and clear wants, wishes and ideals outside of anything his mother told him. It's not like she let him do whatever he wanted even in this stage and while she could've told him that he would be the next padişah, it's hardly this what completely motivated his future behaviour, even lesser so "doom" him.
From my rewatches, I noticed that Mahidevran shows the belief that Mustafa is the main heir to the throne more to others (especially Hürrem directly in E17, E45 and E50 and indirectly in their E69 and E75 farewells, to name a few examples.) than to him, but there are times where she tells him that and one could argue this could've impacted him a little. Some remarks were certainly innocent like the E01 interaction you mentioned and E12's "How will you become a padişah if you're lying in bed all day?", but in quite a few scenes she does call him "the first heir" and tells him that he's the future of the empire and that he'll be the one to rule this world one day. (like E07; also in E55, E95, E101 etc.) The entirety of Mehmet's birth comes to mind as this one time the mindset is fully capitalized on: that was a serious blow for Mahidevran and it's when Mustafa began to question how valued he'll be by his father from that point on. Mahidevran immediately began to assure him that he shouldn't worry, that he's the true heir, but it seemed more like she was assuring herself of this fact than she was leading the kid to believe stuff that may not be possible. While she seemed to begin to grapple with another prince being born after her initial bitter instinctive reaction of it which made her immediately cling to Mustafa, the one lion and treasure she has (immediately kicking out the cariye that sent her the news, not wanting to attend the celebration.), deep down, she was as uncertain as Mustafa was; the future wasn't as clear as she may have wanted it to be. Look at what she told Mustafa after he openly voiced his concerns: "You'll be (the) padişah. Ibrahim promised me." She had to move forward relying on a promise, not a sheer conviction. She told Mustafa this as a means to call him down, since she saw how his worries were overwhelming him, not to make him believe he's the center of the world and that he's unstoppable. That goes for almost all cases where she doesn't use this innocently - it's either to calm him down or lift him up. It's more demonstrative of Mahidevran's own train of thought about how one day this whole torment is going to end than the one of her son. This is something additional Mustafa can get motivated by, sure, the belief that he's the future of the dynasty could've helped him make decisions immediately when he thought he should, even if it meant disregarding his father's will, convincing him even more to do what he did, staying silent where people chant "Long live sultan Mustafa!" in E120-1, perhaps being used to hear how he'll rule next. But it's not the whole picture. That belief is not something he capitalized on, either, despite of his moments of little, but never dominating jealousy towards Mehmet, since he tends to go by his own accord and rely on his own judgement, and this is not something Mahidevran approves.
Mahidevran doesn't make him think that everything is going to be handed to him on a silver platter, either. She makes efforts to make him understand that his brothers are also his rivals for the throne as early as E44 and that he has enemies after him in S03 and S04, which is why she wanted to know his every move and warned him to be wary and not slip up when it could be advantageous for Hürrem and Rüstem. She even told him that Mihrimah and Rüstem could put Mehmet on the throne in E103. She sees they have to fight, as shown by E101 especially. Yes, Mahidevran strongly believes in the exit of that fight, but also that they can get there only through patience, carefulness and being there for each other. Mustafa did what he did when his motivations grew into the stubborn wish to prove himself to his father, believing in his love and fairness. Look how throughout the show he addresses him more with "father" than with "your majesty"? That shows how much Mustafa wants to have and preserve the familiarity of his relationship with his father, along with his principles, that's mostly why he's so sure of himself, which helps increase SS's doubts of him.
Additionally, Mahidevran has never ever lead Mustafa to believe that he's above his father. It's quite the opposite- she always tells him not to question his decisions, especially in S03, and clearly and explicitly underlined the difference between them in E75 when Mustafa recalled SS marrying Hürrem regarding his own decision to marry Helena: "Your father is not a prince." Even when she inadvertently made Mustafa stand against his father due to her words in E48, she retracted that an episode after, realizing her mistake and saying that what's done is done and he should forget how SS upset her. (Yes, she was scolded by Valide then and that could be a factor, too, but Mahidevran has grown more confident in herself in this arc of hers and here she can already disregard Valide if she doesn't agree with her, as seen in E53.) Telling Mustafa that he's above his father wouldn't be something she'd be okay with, since it contradicts her view of the traditions and she's well aware of the possible consequences of something like that, as seen by her quick concerned reaction to the scandal between SS and Mustafa in E29. She hasn't done it even in S04 when her feelings for SS were all but charitable. She definitely has told Mustafa not to think of the possible hole between him and Süleiman, but that's reassurance when he's down, not a confirmation of some superiority Mustafa has over SS. She also compared his experiences to SS's Manisa antics in E97, but she stressed their similarities as şehzades, not as a padişah and a şehzade. So yup, such a statement is totally false.
Many factors contributed to Mustafa's demise, the main one for me being Süleiman's increased paranoia and fear of his son (and after all, he made the final decision), so blaming Mahidevran and Mahidevran alone (or only Hürrem, Rüstem or Mihrimah for that matter) is NOT right. It's far more intricate and complex issue to dump it just on one person and I hate this popular and continuous tendency of people doing it. These comments truly become wild because while this whole belief of Mustafa becoming the padişah (nevermind that Hürrem tells Mehmet this, too?) is part of it, it's still such borderline oversimplification it erases the impact this plotline has.