When sending out the registration emails, the profile isn't linked to the user yet, so in \profile_tokens when fetching the profile around line 50, there is no profile to be loaded.
Create a profile type, add in on the registration form. Use a token from that profile type in one of the registration mails that are triggered.
Have a fallback to fetch the profile because storage hasn't gone through yet at that point.
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It's likely this issue predates Contrib.social: some issue and comment data are missing.
Tested this latest patch on a Drupal 9.5.11 instance running Profile 1.7.0 and it works wonderfully!
We are using #9 in production to send registration emails containing profile fields and it works great.