are runs for that also submitted here? if not, then where?

yes, the PC version of Sonic Adventure 2 is based on the Gamecube SA2B version, and the Battle DLC thats sold on Steam has nothing to do with the changes from SA2 on Dreamcast to SA2B on Gamecube, so the name is misleading, and the Battle DLC also has no effect on any speedruns aside from 180 Emblem runs. All versions go on these leaderboards here

ok thank you