How come Sirius stayed alone during the fifth year?

Question

During Harry's fifth year, Sirius stays, most of the school year, all alone (except for Kreacher, but it's not exactly his favorite companion) at Grimmauld Place.

It seems sometimes Lupin comes and visits, since he's there when Harry use the Floo Powder to "go" and talk to Sirius :

Harry opened his eyes to find that he was looking up out of the kitchen fireplace at the long, wooden tabble, where a man sat poring over a piece of parchment.

'Sirius?'

The man jumped and looked around. It was not Sirius, but Lupin.

but that's all I can remember.

I find it's quite surprising, since Grimmauld Place was still the Order's headquarter, and, during the summer, it was quite a busy place : For instance, Hermione says in her letter:

There's a fair amount going on...

There are meetings, people coming (ang going) : Tonks and Lupin, Snape, McGonagall, Mundungus, once Dumbledore... (plus the Weasleys, who seem to live there for the summer)

Of course the kids went back to school, but what about all the Order's members that were constantly coming? And the Order's meetings?

Sirius would still miss going outside and really "do something", but at least he wouldn't have stayed alone with Kreacher, almost turning mad...

Answer 1

Hermione makes exactly the same point (emphasis mine):

"You belong at Hogwarts and Sirius knows it. Personally, I think he's being selfish."

"That's a bit harsh, Hermione," said Ron, frowning as he attempted to prize off a bit of mould that had attached itself firmly to his finger, "you wouldn't want to be stuck inside this house without any company."

"He'll have company!" said Hermione. "It's Headquarters to the Order of the Phoenix, isn't it?

^{Harry Potter and the Order of the Phoenix Chapter 9: "The Woes of Mrs. Weasley"}

We don't know a great deal about what goes on at Grimmauld Place while Harry is at Hogwarts, but I suspect that Sirius' stir-craziness (and Harry's guilt at leaving him "without company") is motivated more by social (or psychological) isolation, rather than physical isolation.

As noted in the question (and by Hermione), Grimmauld Place is a hub of Order activity, meaning that a ton of extremely busy people are coming and going at all hours, as we observe:

[M]embers of the Order of the Phoenix came and went regularly, sometimes staying for meals, sometimes only for a few minutes of whispered conversation

^{Harry Potter and the Order of the Phoenix Chapter 9: "The Woes of Mrs. Weasley"}

What interaction can Sirius realistically have with these people? They all have things to do, that Sirius can hardly help with in any practical way. Is he going to engage them in small talk, when they're all engaged in literally saving the world? Even if he does get a chance to chat, how long can they give him? A few minutes, maybe an hour at the most?

Once the children all leave, Sirius is stuck with an at-best inconsistent social schedule which, when coupled with the severe psychological trauma of Azkaban, and his continued imprisonment¹, is not a recipe for sterling mental health.

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¹ Of a sort. Even if he's not literally in prison, being stuck inside the same four walls for extended periods of time has an impact