Quod This is because microG doesn't seem to work well on GrapheneOS, and several apps I've tried fail to authenticate login credentials.
It doesn't work because it requires a privileged, insecure function of signature spoofing to be able to impersonate Play Services to apps that expect it. MicroG comes with many security issues, and this is just one of them.
Quod I'm guessing here, but it looks like the best approach is to use the default or (better) a secondary profile with an anonymous Google account to install Google Play, etc...
Yes. If you want to prevent Google knowing your identity, you can try to create a burner account anonymously by going to a place with public WiFi (as opposed to using a VPN, to avoid the phone number requirement), ensuring GMS has sensors permission, and creating the account within the Play Store app.
Quod How much do these Google services acquire information from play store apps?
Only whatever the Play Store apps (or any app for that matter; any app can communicate with any other mutually consenting app via IPC) voluntarily send to Google. Note that Play Services are not necessary for this; any app can just send the same data to Google directly if they include the Google libraries to do so.
Quod Should I use my real gmail account to access emails and other apps that require authentication or will it negate my efforts at using an anonymous google account to install the Google Play services on a specific profile?
If you want to separate your Play Store account from this account, you could either use the web app for accessing your real account, or put your real account into a secondary user profile or a private space. That way, the Play Services process on your phone won't see that you've logged into the Gmail app, for instance.
An acceptable approach is to simply use your real account and install Play Services in the owner profile. It's what I and many users do. It doesn't have any privileged access to the system whatsoever, so the privacy disadvantage of installing it is small. There is a marginal privacy benefit to moving it to a private space (in that it doesn't run when the private space is disabled, and it can't see a full app list), but that does make the setup more complex.