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I'm not sure if it's actually a different manga with the same plot but this one sound familiar with this https://www.mangago.me/read-manga/ai_no_ondo_wo_oshiete_yo/
Exact same plot but the ml is a dentist and the uke is the one who offer to be his sugar baby first.

Hi, guys! I'm trying to find the cute and wholesome yaoi manga I've read months ago, but I can't remember the title and I didn't read it from here. The uke is, I guess, doing a sideline as boyfriend for rent or a sugar baby and then seme is a veterinarian. I think they met when the seme helped the uke from an old man who's also the uke's sugar daddy that time (because the uke don't want to get physical with any of his sugar daddy, I guess). Then that's it, now the vet is offering to be his sugar daddy because I think he never tried dating anyone (or men?). I don't know, but that's the gist if my memory serves me right TwT. Please please, if anyone knows about it, the art is very cute and it's wholesome I swear huhuhu