I was speaking more from my experience with Chan Buddhism specifically, I’ll take your word on how it’s understood in Theravada, since that’s not my background. In the Chan context I’m somewhat familiar with, Buddhism isn’t usually framed as there being only one Buddha in an absolute sense, and figures like bodhisattvas and manifestations play a bigger role in how people understand practice and symbolism. From what I’ve seen and heard, Budai isn’t understood as Sakyamuni Buddha, but is commonly associated with Maitreya, sometimes described as an incarnation or symbolic manifestation rather than literally being “the Buddha himself.” There’s also generally an understanding in Chan that multiple Buddhas exist across different times and realms, so Sakyamuni isn’t seen as the only Buddha to ever exist, just the one connected to our current world and historical period.

I could be wrong and I definitely wouldn't take my word for it but that's my understanding at least.