yes after a reboot stuff gets reopened in the same place it was (sometimes some windows do not, is not 100% stable). but only windows that support saving themselves into the session get reopened, stuff like vscode or Spotify do not. Firefox and kde stuff yes.
Firefox is very stable in this regard, it always reopens all the windows with all the tabs in the right desktops.
the activity part is definitely a bug, its a kde + X bug and it is in wontfix state. i hope they will rework this feature on plasma 6 with Wayland