I have several points that I want to make in reply to this. Prepare for barely-steuctured rambling that's only vaguely connected to your original point(s) ^^
1. About Albus just plain forgetting that acquiring food might be a challenge for Sirius in his situation during GoF
Here's the thing. one of the worst mistakes people make in trying to decipher Albus' actions is to assume that he is indeed omniscient (as was assumed by an 11 year old harry)
he's not. And this is exactly the kind of oversight he tends to make
He himself is so hypercompetent, as well as chronically self-reliant that he quite forgets that other people have needs that he might be able to meet better than they can. Combine that with the fact that Albus seems to have a tendency to get lost in his own thoughts, even when he has company and you get someone who can come off as uncaring and is indeed not really suited to attend to other's basic needs.
Case in point? He and Harry have just swum in the icy north sea and Albus doesn't realise that Harry doesn't know a drying or warming charm until, after a few minutes, he shivers so badly that he can barely speak.
This isn't a character flaw, btw. It's just the way Albus seems to be wired. (And psst, I find this relatable. I try to be attentive bc i care a lot, but it doesn't come naturally to me.)
2. About Albus "wanting to distance Sirius from Harry"
This isn't a point you made op, it's one you cite others making and I have to double down on your point about how ridiculous this notion is.
Throughout book 4, aka Sirius one year of freedom, Albus actively aids him in being as close to Harry as possible. In fact, it always strikes me just how much Albus treats him as he would Harry's parent. At the end of the book, he doesn't just permit Sirius to be present while he interrogates Harry about the graveyard, he actively facilitates him being there. And that's what you'd normally do when you have to question a minor on something emotionally taxing: you get the parent involved and have them be present the entire time.
That's exactly what Albus does here with Sirius, thus very much acknowledging his claim as the closest thing Harry has to a parent.
Book 5 then is a special case and imo an absolute clusterfuck of bad circumstances that lead to a bunch of people making some very dumb trauma-informed decisions.
Which brings me to my next point:
3. About the nature of Albus' feelings for Sirius.
You make the point that Albus loves Sirius and that this is why he kept him hidden. Because whom Albus loves, he seeks to protect and hiding people is how he learned to protect them.
I agree with the latter statement but I'm still debating with myself over whether the first statement is really the only logical conclusion here.
The thing is, you are 100% correct, imo, that Albus protecting Sirius in this particular manner, by confining him physically, follows directly from the way he himself was raised. There is one particular part in the lost prophecy chapter that always makes me stare off into space for like 5 minutes straight:
“Yeah, he did hate it!” said Harry [...]. “You made him stay shut up in that house and he hated it, that’s why he wanted to get out last night —”
“I was trying to keep Sirius alive,” said Dumbledore quietly.
“People don’t like being locked up!” Harry said furiously, rounding on him. “You did it to me all last summer —”
Dumbledore closed his eyes and buried his face in his long-fingered hands.
There is so much in this short passage. Harry starts off by, rightfully, stating that being locked up in the house of his childhood traumas was abysmal for Sirius mental state and that this did contribute to his reckless behaviour (though tbh, I think Sirius would have come to the ministry to save Harry in any situation no matter his own state of mind. Denying that gives Sirius too little credit. Though Harry not seeing that in this moment is understandable)
And i find it remarkable that after the way Albus mannerisms have been described in this chapter so far (calm, detached, almost cold), it is here that he seems to first melt and then crack. Obviously, "quietly" doesn't carry a lot of emotions in and off itself but coming off the previous descriptors of Albus' mannerisms, it comes off as almost meek, like Harry's outburst suddenly and finally pentrates his many emotional walls and he feels the need to justify himself.
And then Harry really seems to strike a nerve with "people don't like to be locked up! You did it to me all last summer —"
There are few interpretations I'm as set on as Albus very suddenly and violently being reminded of what that feels like and that's why this is where the ice around him cracks. (Because when Ariana was locked up it ended in disasters. When he himself was locked up it ended it disaster.)
I'm repeating myself but this is where Albus suddenly doesn't manage to be detached anymore. He's tried so so hard. But he knows this feeling and he knows this pattern and as he later says he's fallen into the trap he had forseen and still he didn't manage to avoid it.
And that trap ... was loving Harry.
And here comes my point: because I don't think him protecting Sirius by keeping him locked up somewhere safe is necessarily evidence of him loving Sirius. It's evidence of him loving Harry.
Because, as stated in point two, Albus knew full well that Sirius had very quickly grown to be one of (if not the) most important parental figure in Harry's life and in protecting Sirius he was protecting Harry from loosing one more person he could emotionally rely on.
Best laid plans and all that ...