chock-a-block does that profile run background tasks while I am in my primary profile?
Your use case is perfect for using a secondary user.
GrapheneOS adds an 'end session' button to the lock screen and power menu of secondary user profiles, which logs you out of the profile, encrypts the data at rest, and switches back to the owner profile. When you do that, none of the apps in that profile can run in the background, including Google Play Services.
GrapheneOS has also recently added an option to prevent a secondary user from ever running in the background. So even if you don't press the end session button, by switching to another profile, all apps in the secondary profile will be stopped entirely. You can enable that feature from your owner profile: Open Settings > System > Multiple users > Name of your secondary user, and disable the toggle 'Allow running in the background'.