[BUG] WebDAV sync/backup conflicts with browser cookies #1297

Problem Description

I'm trying to backup or sync settings to my Nextcloud server but I'm having issues.
The thing is, I'm logged into my personal Nextcloud account in the browser and I want ScriptCat to sync to a different account. But the sync or backup fails with 401 Unauthorized (I see that in DevTools).
If I log out of my personal account on the Nextcloud webpage and run backup again, it succeeds. And when I return to the Nextcloud webpage I'm logged in as the "sync" account now.
The extension and the normal browser share cookies and this is the results of that (I can see all the cookies in the request in DevTools).

Similar, albeit not as obvious, thing happens if I'm logged into my personal account on the web and try to backup/sync into the same personal account using "app password" - backup fails too, until I log out of the web, run backup again and it succeeds. Back on the web and I'm logged in! (bypassing 2FA but I guess that's the point of app password in the first place; but the cookies shouldn't transfer from the extension to the normal browser).

I tried doing similar thing in Violentmonkey (logged into my personal account, backing up to the "sync" account) and it didn't have the problem so I think separating cookies should be possible. (I checked DevTools too and the request in Violentmonkey does have a different cookies, it also sends this using background page unlike ScriptCat which does it in options.html)

Reproduction Steps

1. Log into your Nextcloud account on the web
2. Use a different Nextcloud account in the ScriptCat backup or sync.
3. Start backup
4. Fail

ScriptCat Version

1.2.6

Operating System and Browser Information

Windows 10, Vivaldi 7.8.3925.81

Additional Information (Optional)

No response