If I have a Poliwag and a Poliwhirl and a Poliwrath all on my bench, does Politoed's "Lordly Songleader" attack do additional damage for each one?
Yes, you get the additional bonuses once per Pokemon named in the attack, which you have on your bench.
Source: Lost Origin FAQ; TPCi Rules Team (2022-09-08)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH11_32
SWSH11_32