Hi there, welcome!
AzureStriker14 Will this OS let me continue using and installing APKs after Google starts restricting it this coming September?
Yes, the change is only for versions of android that are "certified" which GOS is not.
AzureStriker14 Will this OS let me keep my eSIM and carrier (Google Fi)?
Your eSIM? absolutely.
Your carrier? Probably. There are quite a few people using Google Fi, without issue, however, there was a post recently of someone using Google Fi who did not have SMS service (it's unclear if they had phone service). This is likely a one-off thing that is fixable, but just wanted to warn you.
AzureStriker14 Will I still be able to use certain apps and games from the Play Store, such as Punishing Gray Raven?
The play store and play services are not installed by default, however, using the GOS App Store they are easily installed. I don't know that particular app, but most apps from the play store will work without issue.