I decided to go into the raws and check out the "I stan that" line, though my JP isn't really great so take this w/ a grain of salt.
The original quote is "そんなの推せる" (Sonna no oseru). "Sonna no" means "something like that" w/ the no particle added to make sonna a noun (since on it's own, it's an adjective). Oseru (推せる) is the potential form of the verb Osu (推す) which in this context means "to support." Putting it together, we get a sentence like "I can support something like that."
The thing that makes this kinda iffy for me personally is that "sonna" can also indicate strong feelings towards something. In context, it does appear to be strengthening the statement, but this is where my lack of JP experience comes up since I can't be confident about it. Personally, I just defer to the translators here, who are probably better than my N4 ass. It could be worded better, but "I stan that" is relatively accurate.
EDIT: Whoops I just realized I spent 30+ minutes on this trying to decipher the secrets behind sonna. This is why I don't scanlate lmao.