Not reflect correct page when click link button to switch page in multi-sites

Description

The issue seems to happen in IE/Edge but not in Chrome.

Steps to reproduce
In alloy templates:
1. Create a new start page (named start2)
2. Create a subpage (named linkpage) to start2 that is a shortcut to the normal alloy start page.
3. Configure muti-sites with start2 as Start page
4. Click the linkpage.
Expected: Navigate to start page of site 1 and the page tree to have switched to the correct page and you can edit.
Actual: It shows the correct data in the iframe but you can't edit and the page tree is not updated.

In music festival:
1. Open a music festival site > Create a PageA with 'Landing Page' page type, Link to Artists list = Artists page
2. Configure muti-sites with PageA as Start page
3. Open PageA in Edit mode > Click on 'ARTISTS' link button to go to Artists page
Expected: Artists page is rendered successfully
Actual: Content of Artists page is displayed. However, the page tree, breadcrumb, and 'All Properties' reflects PageA, but not Artists page.
More details, please view the attached video.

NOTE: This also occurs in the previous release