Edge sync failing on desktop

Your restart test is useful: signing in obtains the key, but the next browser session does not retain a working sync state. That observation does not identify the underlying cause, and I cannot confirm a specific regression or guaranteed fix for build 156.0.4314.56.

Before changing sync, export your favorites from the favorites manager as an independent backup. Then open Settings > Profiles > Sync and use “Re-sync data to this device.” If the problem persists, select “Still having sync problems? Try another option,” then “Reset sync.” Keep Edge open until the reset fully completes; do not interrupt it with the restart test.

After completion, restart Edge once and compare the sync state and key indication. If the same failure returns, add those before-and-after observations and the reset result to your existing feedback report. This is Microsoft's documented sync-recovery workflow, rather than a recommendation to sign out after every launch.