Unfortunately there seem to be no log entries for this. No errors at least, and I used the following in the logger: homeassistant.components.esphome: debug.
Okay, I was silly. The problem was simple to fix and I caused it myself.
ESPhome is an integration AND and addon. I forgot about that last part. So the logs were easy to find on the addon config page.
There was a duplicate entry under wifi_passwords in the ESPhome secrets.yaml. Removing the second entry solved it immediately.
To be fair, if checks are built in to grey out the ‘adopt’ button, it would be easy to add the reason why it’s greyed out and it would improve UX. Will create an issue on GitHub when I find the time.