Over-the-air live data stuck on "Registering"

🚧 THIS IS A TICKET MIGRATED FROM UPVOTY. The original ticket and comments will be available for a limited time over at:
https://abrp.upvoty.com/b/report-a-bug/over-the-air-live-data-stuck-on-registering/
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After linking "Over-the-air live data" for my Tesla, the Live Data page for my car is stuck showing "Registering / Mytesla status".

I added my car to my account and then clicked the blue "Add live data" button to connect "Over-the-air live data". I then clicked "Link Tesla" and entered the Refresh and Access tokens for my Tesla account. I then selected my car, which correctly showed the name of my only Tesla. After that, the blue "Add live data" button changed to a red "Unlink" button, but at the top of that page, it shows "Registering / Mytesla status". I've refreshed the page several times and waited several minutes but it doesn't change. I also tried unlinking live data and then linking it again by entering my Tesla login credentials instead of tokens, but the same thing happens.

The next morning, "Registering" changed to "Not connected", although the red "Unlink" button is still there.