Switching tabs in a library doesn't change the `tab` URL parameter

[Kladki]

Describe The Bug

When switching tabs in any library view, the tab URL parameter doesn't change, meaning that when you refresh or share the page, you end up on the page that you originally started on

Steps To Reproduce

1. Click on any library from the home page
2. Switch tabs (e.g. to "suggested", "genres", etc.)
3. Reload the page
4. End up on the tab you started on

Expected Behavior

The tab should not change when refreshed, by changing the tab parameter whenever the tab changes.

System (please complete the following information):

• Platform: Linux
• Browser: Firefox
• Jellyfin Version: 10.9.8

Example

https://github.com/user-attachments/assets/0f1ecf4d-336f-474d-a7e0-4f9f4defadc1

[prsantos-com]

Confirmed that this bug exists today in master.

It mainly has to do with how navigation occurs. When selecting any of the link tabs, navigation occurs through the ControllerFactory.

If you select any of the links in the side bar, then navigation occurs through the appRouter, which will appropriately change the route and by default, set the tab parameter.

[viown]

Note that this works as expected on the experimental layout.

[prsantos-com]

With that being said, does it still make sense to fix this bug? I'm wondering, because if the experimental layout will no longer be experimental soon, then maybe it doesn't make sense to fix.