Facing the exact same issue, after clicking on "reset sync" button was able to replicate the issue on other account as well. I don't know why even ship feature which can break whole account. Sync won't work on different device or different version of edge tested it myself.
Chrome looking better option right now or Mozilla.Some other users also facing same issue but nothing so far over a months now.
Reddit -Sync settings greyed out : MicrosoftEdge (reddit.com)
-Sync not Working : MicrosoftEdge (reddit.com)
MS community - Synchronization problems; I can't activate synchronization. - Microsoft Community
-edge browser synch stuck - Microsoft Community
-Sync not working. - Microsoft Community
-MS Edge is not syncing, re-sync or resetting. - Microsoft Community
Same issue here. No one cares, it seems at Microsoft. I shared my screenshot via feedback option in edge number of times. Nothing till date. Facing this issue now since more than a month. I even changed the password. Deletes all history and activity - both from browser and by navigating to account.microsoft.com/privacy. Using two browsers at a time - Chrome because it syncs across OS - I have dual booting with Windows / Linux and Edge because all my bing ai chat history is linked to this account - I use it regularly for coding help.