although I say; even though one might call it
Used to soften or qualify a preceding statement, often introducing a contrast or limitation. Equivalent to 'having said that' or 'that being said'.
彼は医者だ。と言っても、まだ研修医だけどね。
He's a doctor. That said, he's still just a resident.
料理が得意だ。と言っても、簡単
When I say 'trip', it's really just going to the neighboring prefecture.
I'm good at cooking. Although, I can only make simple dishes.
Even though I say I'm busy, I do have time to rest.
とはいうものの is a slightly literary way to concede a point before contrasting it, whereas と言っても is more casual and conversational.
でも is a plain contrastive conjunction meaning 'but', while と言っても specifically re-evaluates or limits the strength of what was just said.
Combination of the quotative particle と, the verb 言う (to say) in its te-form, and the particle も (even). Literally 'even saying that', it grammaticalized into a conjunction meaning 'although one says'.