Good example of being confidently wrong. You are thinking of the little Basic interpreter that was on the pack-in consumer demo disc. Not the Linux Kit which was a very real initiative and had universities involved. We were using them in a big dedicated lab.
Not at all, you're mixing up with YA BASIC, that came with PS 2 demo disc.
People that weren't there keep mixing channels on this one.
To acquire PS2 Linux, you had to pay additionally 300 euros for the Linux distribution, the PS2 hard disk, and cables that would only work in monitors using sync on green signal.
Initially the price was much higher, and got reduced to around 300 in 2004.
I don't know -- per Microsoft's recent announcement.. the Xbox will basically be a Windows PC in a tiny package. So, no more Xbox Live needed to play online and you can install other marketplaces on there (such as Epic and GOG).
Microsoft hasn't announced the next Xbox yet. They've been promoting the Xbox-branded ROG Ally this cycle, which is just a Windows PC in a tiny package, but that's not the next console, just a current generation SteamDeck competitor.
They've been implying there will be a greater convergence in which Windows devices feel (play) like an Xbox, but they've been saying the same things since initiatives like Xbox Play Anywhere originally launched in 2016 (almost a decade ago!), which didn't result in the Xbox Series X being a PC in 2020 (despite similar speculation that it might be at the time).
It will be interesting to see where Xbox is planning to go, but so far most of the speculation is just reading (decade old) tea leaves.