I think you should try stating your wishes, and then sticking with them. It worked for me before, when I was also struggling with a similar thing, thought it was needy grownups, instead of kids.

If you say things like “not right now”, “I’m doing x currently”, “I can’t because I’m busy”, this signals to them that they need to wait, and you will be available later. And as they get impatient they will ask you again. This isn’t what you want.

If you say “sorry, today I would like to play alone” they will possibly be more disappointed that they don’t get you at all, but at least they will know not to expect your availability and they can hopefully make their own fun. It’s sort of like ripping off the band-aid. It’s more uncomfortable for you to say it this way, and will hurt them more to hear, but it’s better for everyone involved in the long run.

I used to be evasive with my adult gaming friends, like “I’m not sure I’ll be online today” and “I might come on later”, sometimes while hiding my steam and discord status and playing alone. But it had the same effect you’re describing. These days I just tell them, “Sorry I’m too tired”, or “Sorry I feel like playing a single player game today”. It’s miles better, and I don’t have to keep lying.