Four is possible in many ways:
aiery canst dolma offal
realo tings dampy humph
raine scold bulgy ought
ureas gilpy cyton conic
lutea prosy canid cigar
leary ungot camis humph
stale groin dampy humph
If you're wondering what some of those words mean, Wordle (and this variant) have a big list of fake words it allows for guesses.
I think 4 is probably optimal, but my solver is still running. :) There's probably way more fours as well, my solver only prints new bests found, and this list is from progressively allowing a wider and wider search, so each result is from a separate run. I wonder how many end in 'humph'.