You sure that’s RF, the remote looks just like the generic ones they use with cheapo IR controlled RGB strips?
If it is, you could probably use it with an RM Pro in the same room but beware that they use a lot codes that are the same as those used by other devices, for instance, a lot of Xbox IR controls trigger changes in these.
Oh whoops my bad… well even if they are IR the rm pro can control them? Would it work? Or would it just be better to spend a bit more money and get the wifi bulbs?
What wifi bulbs are supported by home assistant (cheap ones), or directly supported by google home?
My advice would be to spend a bit more money and don’t go for cheap unknown/unsupported devices unless you’re willing to spend time on it to get them working.
Broadlink RM Pro has a IR & RF learning feature. You can teach it with the existing IR remote of the RGB bulb. Check out the “Broadlink RM Pro” HA Component.