I experimented a bit for this task, but none of the options was side effect free. I decided not to move forward with this work, as I was not sure it could cause unexpected bugs since we still have some issues with the stability of reading lists T316710 and are currently testing sharing reading lists.
I'm listing some of the attempts, so it's documented and hopefully helpful when another engineer or I pick this ticket in the future.

The warning is caused by the taskGroup.wait() calls in a thread other than main. Since we have code that explicitly sends CoreData operations for the background, it's impossible to have them executed on the main thread. Changing this would require a complete overhaul of our current implementation.

• Swift task groups (ref https://developer.apple.com/documentation/swift/taskgroup): this approach takes advantage of the existing task groups and the possibilities of concurrency on swift. This approach would be a good alternative to the current implementation, as it allows for safely performing the asynchronous tasks. However, a more significant refactoring of the code would be required since the background sync tasks were only sometimes properly executed with my approach of not rewriting large parts of the code.
• Removing the wait statements resulted in larger syncs (syncing several lists/lists with many items) not fully syncing with no error propagation.
• Rewriting code to force a synchronous code order: this option also resulted in some inconsistency in the execution of the background tasks. I experimented a bit with this task, but none of the options was side effect free.