If you look at their conversation in the last episode, especially the body language, you can tell Culber wanted to reach out to Stamets, probably in part because of Cornwell's (RIP) and Reno's advice. The whole "I'm going to the Enterprise" bit seemed like an afterthought to justify him coming to the Spore Chamber in the first place, and probably not what he wanted to say originally.
It's so classic, it's a trope: Two characters start talking, A lets B go first, B says something that throws something A said (but at this point doesn't actually believe anymore) back in their face, and A quickly changes what they are saying to match.
Culber spend part of the season pushing Stamets towards moving forward (not because the love wasn't there, but because of his own disassociation and trauma). And now that he wants to tentatively reach out, Stamets has decided to do so (despite very clearly still having feelings for Culber). I'd have to rewatch it to be sure, but I remember Culber's face when Stamets tells him that, and it looks like a man thinking that it would be kinda scummy to have pushed him this far and then going, "you know what? Now I wanna go back." So instead he tells him that "forward motion" is a great idea, all cool kids are doing it, including me.
So it's really not that surprising that later on he goes "what the hell am I doing? I love him, he loves me, and I'm never going to see him again" and goes back.
