Is the Shimano UN55 bottom bracket in 68x122.5 and 68x127.5 sizes JIS square taper?
It is JIS.

Shimano doesn't have separate Italian taper cranks, and it does not make sense to them to make BBs that do not fit their other products. Italian taper has been practically obsoleted since Campagnolo switched to two piece cranksets in the 2000s. If you manage to find one now from a competent vendor, it will be clearly marked as one.

Regarding your experience buying online, it does not sound like the vendor did know what they were doing.