Looks like a profile-specific problem. Could you please try the following suggestions:
- Repair Microsoft Edge. Go to Control Panel\Programs\Programs and Features --> Microsoft Edge --> Right click and select "Change".
- Remove your current 2 profiles and re-create them. You may need to turn on sync first in case of any data loss.
- If it is still not working well, remove the entire User Data folder. Navigate to %localappdata%\Microsoft\Edge on your computer, end all Microsoft Edge tasks in Task Manager and delete the User Data folder. Then recreate new ones.
If the suggestions above can't fix this issue, please consider assign a preferred profile for your target site. This would work in the same way as you've expected. In the meantime, please report this problem to the Edge Dev Team by sending feedback (Alt+Shift+I).
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Best Regards,
Shijie Li