Update: I can confirm the 2023.12.4 Update worked for me.
My case was, I thought, completely useless, as I had previously ‘Verified’ my phone number, and struggled for weeks to no avail.
For those that are still having trouble authenticating, these are the steps I took to resolve this
[I had previously verified my phone number, so in the account section of the app, there was NO mention of password anywhere. No way to reset it etc.]
Ensure ALL traces of existing life360 patches are removed from HA. You will need to search around here for instructions on how to do this, and don’t forget to restart HA.
log out of the Life360 app on your phone.
Go to the Life360 Password reset tool here: Life360 : Reset Password. Click Search by Email
This will then ‘Send a Text to your mobile Phone’. Within the text (amongst other stuff), is a link to Reset your password. Click on the link, and reset your password. What this automatically does is to un-verify your phone number. This is what you want.
When you log back into your app (It again didn’t ask for a password, it texts a number to your phone which you then provision), you should notice your account is now set to unverified - This is our goal. DONT verify it!
From that point, in HA, discover the official life360 integration, and re-provision. This worked for me.