[4.x]: Selecting a different site in the CP Entries view doesn't update the sidebar links

What happened?

Description

In a multisite set up, when I'm looking at the list of entries (for Site A) in Craft's control panel and I select a different site (Site B, let's say), I would expect clicking "Globals" or "Assets" in the sidebar to take me to Site B's globals or assets, instead those links still take me to the globals or assets for Site A.

If after selecting Site B from the sites dropdown I refresh the page, those sidebar links do get updated as expected.

Steps to reproduce

1. Have a multisite set up
2. Navigate to the entries page in the control panel
3. Change sites with the dropdown
4. (don't refresh)
5. The links in the sidebar still link to the first site (not the site that you switched to)

Expected behavior

1. The sidebar links should link to the respective page on the site you switched to.

Actual behavior

1. The sidebar links still link to the site that was selected before you switched sites – unless you refresh the page, then it works as expected.

Craft CMS version

4.5.5

PHP version

No response

Operating system and version

No response

Database type and version

No response

Image driver and version

No response

Installed plugins and versions

No response

Reproduce the issue in the control panel Entries view with a multisite setup by switching from Site A to Site B without refreshing. Trace the site dropdown change and sidebar link updates; done means the Globals and Assets links target Site B immediately after the switch.