Filter management broken in Firefox private mode

Environment

• OS version: Ubuntu 20.04
• Browser version: Firefox 100
• Extension version: Adblock Plus 3.13
• Last working version: Adblock Plus 3.12

Steps to reproduce

1. Open about:preferences#privacy.
2. In the History section, select "Use custom settings for history" and select "Always use private browsing mode".
   Note: Selecting "Never remember history" should have the same effect.
3. Install test-mv2 extension.
4. Go to about:addons and click on the test extension list item.
5. Change "Run in Private Windows" to "Allow".
6. Install Adblock Plus.
7. Make sure that "Allow this extension to run in Private Windows" is checked, so that the extension icon is active and its icon is shown in toolbar.
8. Open settings page.
9. Add a filter list and a custom filter.
10. Reload the extension.

Observed behavior

• After 7) Error message is shown in background page: "DOMException: A mutation operation was attempted on a database that did not allow mutations."
• After 8) No filter lists are shown as installed.
• After 10) No filter lists are shown as installed and there are no custom filters shown.

Expected behavior

• After 7) No error message is shown.
• After 8) Default filter lists should be shown as installed.
• After 10) Newly added filter list and custom filter should be shown in addition to default filter lists.

Further information

This regression was originally reported as https://gitlab.com/eyeo/adblockplus/abc/webext-sdk/-/issues/231.