Short answer - I don’t know for sure, the other post has my ZHA upgrade experience written up in detail.
Longer answer - After restoring the RPi4 backup to the Yellow, and installing a “new” Zigbee integration, the ZHA migration tool seemed to kick in.
The trouble is, details matter. My experience was with ZHA not Z2MQTT. Apparently, not all Zigbee coordinator radios operate the same, meaning migrations may not work. The integrations have different drivers for different chipsets, and these have complex dependencies. No, I don’t know what these are, sorry.
EDIT: Found the lost discussion thread, with lots of technical detail on the pitfalls of migration:
If you start the ZHA coordinator migration tool manually, it appears to assume both the old and new coordinator are both accessible so the details can be transferred directly (i.e. not via a HASS backup). This is why it wiped the old coordinator (no, I don’t remember it giving any warnings).