So I'm going to preface this by saying if its incoherent it's cause I'm currently in a race to write this post before my sleeping medication knocks me out.
Anyways, I, in my terminal Donna Noble brainrot, had a realization. I think one of the reasons that Ten gets so, so incredibly attached to her (as attached to her as he is to Rose, possibly more I'd argue), is because she reminds him so much of the Master.
Yeah, she's meant to mirror him, but so is the Master. The Master was his childhood friend, the only other person who ever understood him that fully, and he and Donna honestly share a lot of traits. They're both self-absorbed, headstrong, and incredibly lonely. They both tend to lash out at people, and they both tend to have very limited worldviews. Also lbr they're both incredibly dramatic people.
The difference is, Donna is, ultimately, a good person, and while she probably sometimes feels wronged by her lot in life, she ultimately wants to make the universe a better place. The Master, on the other hand, wants revenge, and they want to hurt the universe for wronging them.
Donna is what the Doctor has always wanted the Master to be. Someone who knows them so well and who shares their vision of how the universe should be and how they can help.
And coming into series 4, Ten believes the Master is dead and gone, that he'd lost his oldest and best friend in the universe, and then Donna comes swooping in, all fire and sass and incredibly annoying stubbornness, and such incredibly deep-cutting questions that he's not used to because only one person in the universe has ever known him well enough to ask questions like that.
Ten is a lot more expressive around Donna in a way that he's certainly not with Martha and I'd also argue not with Rose either. With Rose it was about love. It was about how bright and shining and beautiful she was and how the Doctor, with all the blood on his hands, could never be like that. He would follow her to the end of the universe and back because she's such a beacon of good, but he's very reluctant to share those darker parts of himself with her.
Donna is very much not like that. She's flawed. She's self-absorbed and selfish and oftentimes puts her needs above everyone else's. When she and Ten first meet she's kind of a terror. In short, she's not perfect, and i think the fact that she does have those flaws and those ugly bits makes Ten feel a bit more comfortable with being really, truly himself around her. She watched him commit genocide the first time they met, they can't really get much darker than that.
So he's sillier, he's more physically affectionate, he's more open with his issues and he's more open to letting Donna pry into his issues. He's still an emotionally constipated weirdo but so is Donna, and she relates to him on a level that only the Master ever really could.
Also, honestly, there's an element of control there that the Doctor has never had with the Master. The Doctor is an attention whore, they love to be in charge and love when people listen to them. There's always a power imbalance between them and their companions, and even though it's less with Donna because she only puts up with so much bullshit, it's still there. He still has the ability to do things that he probably would never be able to with the Master, simply because she's a human, and i do honestly think he likes having that power. It's always been a thing with the Doctor that he's very much tempted by power and loves being the smartest person in the room. The Master was, by a lot of accounts, smarter than the Doctor in a lot of ways. They did better in school and Three even calls the Master a genius.
Donna's very smart in a lot of ways, and in ways that really complement the Doctor's strengths, but she was never Ten's intellectual equal like that, not without the meta-crisis. The thing that made her and Ten work so well together was always her emotional intelligence and people skills and her being so down to earth.
Which, clearly, are skills the Doctor has never seen as particularly important for they themself to possess.
Idk exactly where I'm going with this other than Ten glomped onto Donna because he'd just lost his best friend in the universe and she was the absolute perfect person to fill that gap and she probably reminds him a lot of the Master and now they're inseparable, just like the Doctor and the Master are