When I select a model (such as Claude 4 Sonnet) and/or toggle "Entire Web", when I refresh the page it does not retain those settings. It reverts consistently to "Code" (which cannot be deleted from my Custom Assistants) and "Entire Web" enabled.
Just after setting:

And immediately after refresh

MacOS, occurs in Firefox and a minimal Chrome installation across multiple machines.
It should retain the last model used at least within that browser. This was (usually) the functionality until recently.