I can't help but think that a lot of sci-fi games I'm playing or at least aware of tend to take inspiration from 20th century futurism these days.

Examples of such are computer games like No Man's Sky, which draws on 60s and 70s sci-fi, and Elite: Dangerous, a game I don't play, appears to take inspiration from 80s sci-fi.

I liked Overwatch for it reminding me vaguely of 2000s action shows I watched like Ben 10, but after watching a video related to Overwatch (sometime during the Busan map reveal with the MEKA fight), I was disappointed to hear that Blizzard admitted they took inspiration from 80s cartoons. While there are aspects of, say, the 1980s aesthetic I like (namely geometric designs), the political climate of the 1980s is now enough to make me resentful of the decade, and the fact that I didn't even exist before 1997 means I find it hard to fully relate and connect to.

Aside from Doctor Who with David Tennant, Halo and AI: Artificial Intelligence, I wonder what would be good examples of films, games, shows and media that included predictions of the future from the mid- and late 2000s' perspective, with minimal artistic inspiration from other decade and preferably without a post-apocalyptic setting?

A lot of sci-fi stuff these days to me seems quite lazy, heavily drawing on cyberpunk and 1980s aesthetics and similar tropes, or post-apocalyptic wastelands. For more unique films like Interstellar, it does kind of feel like original 2010s futurism. I have yet to watch the film but it doesn't appeal too much to me because of how specific the premise of the story is. Avatar doesn't really appeal to me because of how specific the story is too.

iRobot fits the bill for mid-2000s. I loved that movie.

I can't think of a late 2000s sci-fi movie. Most of it would be video games, like Halo (as you mentioned), Mass Effect, Final Fantasy, Crysis etc. A lot of video games take place in the high-tech future so that's where you're going to find a lot of futurism.

iRobot fits the bill for mid-2000s. I loved that movie.

I can't think of a late 2000s sci-fi movie. Most of it would be video games, like Halo (as you mentioned), Mass Effect, Final Fantasy, Crysis etc. A lot of video games take place in the high-tech future so that's where you're going to find a lot of futurism.

I wonder what would be the reason (besides the recession) behind the lack of a late 2000s sci-fi movie. I don't know how to feel about those games you mentioned. I might have to take a closer look at Halo although a lot of the sci-fi stuff is more military related, and I struggle to get into the game now because of personal issues related to envy, with gender. I'll also check out the Deus Ex games if I can, but most of its releases are from the 2010s. Also, I tend to see many things by Microsoft as just uncool - unlike Apple and Google they don't do a good job of appealing to young people, despite MS being one year younger than Apple.

There were many futuristic aesthetics in the early 2000s. Especially in music. Back then, I would listen to a lot Dance, EDM, and Electronic music.

These were a couple of my favorites:

Rockell - What you did to me(Linus Mix)(2001)
pkzTzZuZyOY

Amber - Anyway(Men are from Mars)(DJ Encore Club Mix)(2002)
3AOpRHKP-k8

There were many futuristic aesthetics in the early 2000s. Especially in music. Back then, I would listen to a lot Dance, EDM, and Electronic music.

These were a couple of my favorites:

Rockell - What you did to me(Linus Mix)(2001)
pkzTzZuZyOY

Amber - Anyway(Men are from Mars)(DJ Encore Club Mix)(2002)
3AOpRHKP-k8
I prefer more mid and late 2000s stuff but I can look at these too if and when I can. I have a vague idea of what the early 2000s thought the future looked like, only if because recently social media seems to be paying more attention to that time.