Whatever you go with, make sure to look not just at “MIDI sync” but also “MIDI quantize”
A looper that will start at the start of the next quantized bar means you won’t have to be super accurate on the foot switch to avoid clicks.
The first Pigtronix Infinity (not v2) is, indeed, one such looper.
Most, but not all, stereo looping delay pedals, sadly, are not.