I think one of the funniest things in the sonic fandom is that the characters debut anniversary is treated as their birthday/vise versa almost impling that there birthdays take place at some point during that game.
June 23 1991
Eggman posting on social media: for my birthday I get to try out my brand new drill tank!
Sonic replying to eggman on social media: for my birthday I got to fuck up his brand new drill tank.
September 23 1993
Amy hiding behind a bush: for my birthday Im going to meet my hero sonic the hedgehog.
Metal hiding behind Amy: and for my birthday I'm going to fucking get you.
June 19 2001
Rouge: happy birthday handsome.
Shadow: thanks I guess?
Rouge: well are you going to say it back?
Shadow: no.
Rouge: the fuck you mean NO!?
Shadow: I just feel like breaking out of prison and trying to sanitize all life on the planet is what I want to think about right now.
September 13 2007
The queen: so princess it's your birthday did you have any plans?
Blaze: oh it's my birthday? no mother I forgot all about that.
The queen: anyway the universe is collapsing into a parallel dimension and will probably kill us all in the next 48 hours you should do your job now.
January 5 2003
Omaga: what the fuck man! egg man made me to kill and destroy I love killing and destroying and what does he have me DO! Guard duty he puts me on guard duty during my birthday >:(
dearest CEO and authority on omega, i seek your guidance for a thing i'm maybe plotting: do you think, in a future far enough ahead where eggman is no longer a thing, omega would take pity on an abandoned metal sonic and find some way to repair him at least enough so he's functional again? or would he be completely apathetic, seeing as metal is/was just another of eggman's robots?
First of all THANK YOU for the acknowledgement. That alone has made my day.
Second of all, as you no doubt predicted, this post got LONG and I put way too many disclaimers in the beginning so here's the TL;DR: current Omega would nuke Metal from orbit, but this is not about being current, so I came up with a few fun ideas for your consideration.
Third of all, a general guideline for discussing Sonic characters in the far future is that literally everything is fair game as long as there's some acknowledgement in the writing of how the character has changed and at least an allusion to what might have caused it. See my strange future Metadow drabble I did a while back for reference- people were willing to accept that Shadow could get really helpless and depressed and that Metal (Neo, in this case) could get actually somewhat emotionally stable given enough time and distance from the Egghead himself. Shadow was really only a small divergence from his established character, while Neo was much larger leap. It was an interpretation inspired by the recent trans girl Metal Sonic movement here on tumblr, which would be difficult to parse without the context of that current fanon.
Now that I've spent all that time on that disclaimer, allow me to throw it all away. Omega doesn't really have any established character interpretations, canon or fanon. It's pretty much just me, the IDW canon, the Archie continuity, and a bare few snippets from the games that you're cherry-picking from. But this means that you get to have FUN. This is your sandbox now! You get to invent justifications for any kind of behavior you want Omega to have!! This is literally my favorite part of being a fandom creator- we get to come up with interesting ideas and convince other people to share our brainrot!!!
Okay okay okay okay okay, with THAT whole nonsense out of the way. . . to get to the part that you actually asked for:
I think it would really depend on just how far in the future we're talking for Omega, and any other people he currently has in his life. Fresh, current, canon Omega would never even think about restoring Metal Sonic in any capacity. If anything, current canon Omega would stomp him even flatter. But you knew this already. You're not asking about current canon Omega- you're here to suggest some hypothetical future character development for him. Allow me to throw out a few personal ideas:
If someone important to Omega took pity on Metal Sonic first (almost exclusively Shadow or Rouge, though there could be others depending on circumstance) then he might not immediately smash Metal for parts. He might even help with repairs a little. You probably knew this already too, though. Omega's look to Shadow while holding Metal at the end of Sonic Heroes probably suggested that idea enough.
But to get to the true vision of your ask, of Omega repairing Metal on his own. . . if said pitying person was somehow incapacitated and left their work to restore Metal unfinished, then I could see Omega completing the repairs. He'd be in denial about it the whole time. He'd probably hate himself for it. But he's got a thing about completing goals, you know, and I think he'd be compelled to do so for someone he was close to even if he's not onboard with the mission. This circumstance would be perfect to set up an enemies-to-friends situation. Omega only tolerating Metal out of love for the original person that cared about restoring him, but that could change over time.
(I'm imagining a scene where a newly-repaired Metal learns about his abandonment and, defying Omega's expectations, gets downright pissed at Eggman for it- and this being enough for Omega to reconsider his views just a little bit.)
The other idea I'm imagining for this concept is a distant future, something like Silver's future, where, for whatever reason, Omega is alone.
(My personal character interpretation of Omega is that he hates being alone, even if he's not so fond of people. He's desperate for the attention of others, even if it's only to run screaming from him. It has to do with being isolated and ignored during his formative period; his deepest drive is to be acknowledged in any capacity.)
Perhaps he's been alone for a long time. Perhaps he's still grieving Shadow. Omega's had a lot of time to mull over stuff and get nostalgic about the "good ol' days". He stumbles across the broken corpse of Metal Sonic and is hit with an idea that he knows would've made his younger self want to blow up an entire city block. He doesn't waste vital parts on restoring Metal, but he keeps the blue corpse around and adds bits and pieces whenever it's convenient. Eventually, perhaps unexpectedly, the repair is finished. Metal could be reactivated. Omega hesitates. He eventually decides that in the worst case scenario, he could always blast the inferior robot to bits again should he prove annoying.
(Scene: Omega flips the switch. Metal Sonic awakens, expecting to see Eggman standing above him. . . only to find Omega. And Metal is distraught about this in a way he can't really understand about himself. Omega, surprisingly, sympathizes, recalling a long-lost desire to be the greatest Eggman robot only to be abandoned all the same.)
I could see this being the start of an almost mentor/mentee relationship between the two, much the same way that Dadow is usually spun, actually; a much older Omega begrudgingly taking care of a Metal Sonic who was deactivated during Sonic's time. The idea interests me- if I wrote it, one of the reoccurring thematic notes would be an exploration of the Omega of now versus the Omega of the past, from Metal's point of view. If you want to throw Silver in there, it could be a more literal comparison, too, which could be fun.
In conclusion: those are just two of the thousands of plausible ideas you could write for Omega and Metal. Honestly, interactions between these two fascinate me so much and I would adore seeing what you might come up for them, no matter which way you spin it.