Hello, Chicago.

I see in my System Settings > Login Items only two Edge-related items: Microsoft AutoUpdate and Edge itself.  I am not aware of any other Edge background processes.

The only way I know to stop the annoyance is to make Edge itself a Login Item and leave it running with one browser window open and minimized to the Dock.  It can be your Start page, or even about:blank.  (The necessity to have a browser window open is due to some change in Edge a couple years which I reported as a bug which I'm not aware has ever been fixed.  If you don't have a browser window open, an error will occur when sync is attempted  )

Yes, you can change your Collection's configuration to sync daily instead of whenever a bookmark is changed.  To do that.

• Open your .bmco document.
• Click the tab: Settings.
• Click the subtab: Syncing
• Click the subtab: Advanced.  (Side effect: This will switch Syncing off).
• In the top table, click the "+" button to add what we call a Syncer.
• In the middle Triggers table, change the first column of the item which appears from I log in to my Mac to Scheduled, then in the next column Every day, then your desired hour.
• Configure the bottom Commands section to have four commands, in this order:

• Import from all   Cancel if not allowed by browser running
• Sort
• Save Document
• Export to all     Cancel if not allowed by browser running

Don't worry about Cancel if not allowed by browser running since these don't apply to modern web browsers – syncing is allowed when browser is running.  For Edge, to the contrary, it's required, which is why are are here.)
• Click the Syncing button in the toolbar twice, to make it paused (red !) and then Ready (yellow dot).