In terms of privacy, you are giving your identity provider insight to each of the third party services that you use. It may seem that there isn't too much of a difference between using Google's SSO vs using your Gmail address to register your third party account. However, one big distinction is that Google would be able to see often and when you use each of your third party services.
Also, it may be impossible to restrict the sharing of certain information from your identity provider with the third party service. For example, maybe you don't want to share a picture of yourself with a service, but that service uses user profile pictures or avatars. That service may ask (and require) that you give it access to your Google account's profile picture in order to authenticate using Google's SSO. You may be able to overwrite that picture, but you also may not be able to revoke the service's ability to retrieve it. If you used a "regular" local account, that Google profile picture would never be shared with the third party service if you did not upload it directly. The same is true for other information like email, first/last/full name, birthday, etc.
There are other security and operational concerns with using SSO options. With the variety of password managers available, introduction of passkeys, and increased adoption of multi-factor authentication, many of the security benefits associated with SSO aren't as prevalent as they were 10 years ago. The biggest benefit is likely the convenience that SSO still brings compared to other authentication methods.
Ultimately it's up to you to determine if these concerns are worth the benefits of using SSO (or the third party service provider at all if they require SSO). I have a feeling the common advise will be to avoid SSO unless its an identity provider that you trust (or even better - one that you host yourself) - especially if you're using unique emails/usernames along with strong and unique passwords with multi-factor authentication and/or passkeys.
This is definitely the wrong answer for this community, but may be an acceptable answer for this post. I have never used it nor would I ever recommend using it, but the conversations I have had with others who do use it make it seem like the service is far better than any alternative. Given the OP's requirements and willingness to both pay and sacrifice privacy, it seems like this may be appropriate for OP.
I would still explore other options though. There are several competitors to Life360 and presumably there are some with better privacy policies (even if the service would not typically be recommended on this community). Maybe OP could use a service like https://tosdr.org or https://tldrlegal.com to better evaluate those options that would likely not get much attention on this community.
Depending on the required features, maybe the Live Location Sharing feature of chat apps like Element may be sufficient. It could also help improve the privacy of the users' by switching to a more private/secure messaging app in the process.