Just to add some further detail, it appears that merely having them have a profession at some point is not sufficient, they need to be a profession at the point of conversion in order to get into a minecart. An unemployed villager will not enter a cart under any circumstance once converted to a zombie, even if they have previously had a job and subsequently lost it due to moving X amount of blocks away or profession block being removed.
Just done some testing of this on Bedrock 1.16.1 creative and survival, both local and on a realm, and can confirm that a villager who has never had a job, once converted to a zombie WILL NOT get into minecart. If the villager has ever linked to a job site (doesn't have to be traded with/locked in) then the converted zombie will get into a minecart as expected.
Whilst we are making villager trades match Java, can we make it so curing discounts are persistent like Java rather than degrade over time?