[Bug] Settings sync on Firefox only works when browser is restarted

[Maelstromeous]

Prerequisites

• I searched for any existing report about this bug to avoid opening a duplicate.
• I can reproduce this bug in a new, unmodified web browser profile with Dark Reader installed as the only extension.
• I understand I need to use the Broken Website Report template if this bug I am reporting occurs on a single website.

Bug Description

It seems that the settings sync for Dark Reader does not "hot reload" the site list, and mandates that the browser be fully restarted before new settings are loaded. In this multi-device world, we should be able to have the site list synchronize and populate itself without the need to restart browsers.

Website Address

N/A

Steps To Reproduce

1. Have two devices.
2. On Device A, add "test2.com"
3. Press "Synchronize now" in about:preferences on device A
4. Press "Synchronize now" in about:preferences on device B
5. Observe that on device B, the site list has not updated.
6. Close and restart Firefox on device B
7. Observe the new entry is now present.

The inverse is also true. The only time the site list changes is when the browser is fully restarted.

Expected Behavior

Upon synchronisation of devices with Firefox Sync, the site list should automatically update.
OR
Provide a button to reload the list.

Actual Behavior

The sites list does not update.

Screenshots

No response

Operating System

Windows & Mac

Web Browser name and version

Firefox 124.0.2

Dark Reader version

4.9.82

Additional Context

No response