hey SRC finally rolled out a change that fixes this... still shockingly late but hey better late than never
this is mentioned in the celeste game-wide rules on this site. in-game audio, including music, is recommended but not required, and strongly recommended for top level runs but still not required. you'll be fine
you can find premade splits files for pretty much every category at https://www.speedrun.com/celeste/resources , those will have the settings handled for you. or if you can get your old .lss file from you old computer onto your new one, that will have all the same autosplitter settings (and also your run history and everything which you might want to keep running against lol)
Just to add to this, i've seen some new runners have the idea that being "good at not dying" is useful. Not dying in celeste speedruns is definitely fast, but I wanna point out that there's basically no such thing as being "good at not dying" in general. you can really only be good/bad at individual strats and tech. So going for golden berries and deathless runs is a cool challenge but it's really unrelated to speedrun practice. you might be great at a set of strats that gets you through chapters deathlessly but that ultimately has almost no bearing on how good you'll be at the speedrun strats you choose to learn afterward.
Just want to confirm, yes Celeste doesn't use real time as a timing method at all and all submissions should leave real time blank. Just enter what you see for the chapter/file time (depending on whether it's an IL or full game submission). Each category's rules will spell out exactly what you need to submit