In my opinion it should be fine. There used to be a runner called AuroraDash that I remember had their own music during run submission videos. But as long as your run is not like elite top 3, it should be fine. I reckon top times would probably be better to have the default music and sound to assist in verification.
I believe a lot of speedruns mute the game music and play their own music and it's fine. Anyways muting the music is generally okay since only the in game sounds are useful for verifying the legitimacy of the run
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
The rules say that top runs must have the in game music, but if its your first run it will probably be fine.
top runs should have the in game sounds, the music is not needed
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