I'm German, and have lived in Britain, Australia and now Singapore. So my English idiolect is, of course, a bit weird. However, I would pronounce 'thought' like the London sample in https://en.wiktionary.org/wiki/thought#Pronunciation They give that as /θɔːt/.

I realize that the American sample on that page does indeed rhyme with 'hot'. They give that as /θɑt/ and blame the 'Cot–caught merger' also known as the 'LOT–THOUGHT merger' which would explain everything.

See https://en.wikipedia.org/wiki/Cot%E2%80%93caught_merger

Of interest here are:

• The LOT set (stop, sock, dodge, romp, possible, quality) (+ shot, hot, cot, bot…),

and

• The THOUGHT set (taught, sauce, hawk, jaw, broad) (+ caught, bought…)

(For those without the merger, there's also the CLOTH set of words (cough, broth, cross, long, Boston) which fall in either the LOT set or the THOUGHT set depending on the specific accent.)

Reading the poem, I was also thrown off because I’m on team shot/hot and thought/bought.

Shot/thought rhymes for my partner though.

Both of us are from the US but opposite coasts.

     It’s American to not give a shit
     about any of this and rhyme
     whatever we want