You should no longer get any copyright issues over using the song in your videos.
When JAM Project first announced the special theme song for Alex, it immediately raised some questions about copyright. When asked directly by Broski, the game's director Takayuki Nakayama stated that they reached out to all relevant parties, and said that it should be fine.
While what Nakayama was undoubtedly genuine, it seems like something went wrong in the chain of companies that handle distribution and copyright, which resulted in dozens if not hundreds of videos getting claimed on YouTube.
Maximilian Dood helped to bring more attention to this matter with a PSA post about many segments of his video getting claimed by The Orchard Music, an American music distribution company.
Seems like Capcom and JAM Project were immediately on top of this, and mere days letter the matter should be resolved, as announced by JAM Project on their official X account.
Maximilian Dood has also posted a follow-up, stating that everything has been resolved.