As far as I understand, these new restrictions only affect sideloaded apps, not apps installed via the Session Installer (“from app stores”).
So the restrictions would only affect the F-Droid client app, and only if you manually download it from a browser and install it, not if it comes preinstalled with your ROM. Apps installed by F-Droid are not affected.
Also, the permissions that are restricted are quite powerful (accessibility, device admin, etc). Not having them should not affect core app store functionality in a meaningful way. So F-Droid client should be fine. And even then, Google has still left an escape hatch (“Allow restricted settings”).
Source: Android 15 cracks down on sideloaded apps even harder to protect users - Android Authority