ok nice!
i tested this on my lay theme installation:
open project in project overlay open page overlay click on a link to a page in the page overlay then project overlay closes, page overlay closes and the page shows uphere u can see it:
https://www.dropbox.com/scl/fi/2hior6cp5q87f5bg4vaab/Untitled-1.mov?rlkey=lmgjdq066fespmmj99wvldgun&st=1jcdcgm0&dl=0
im not sure if i did anything different than you, but this is what is not working for you right mmh