Secondary bridge exit.
Yes, have the captain's chair platform slide to the side to reveal a hatch on the floor.
No need to move the captain's chair aside; there's a perfect open area in front of the Helm/Nav console. I've always pictured a hatch that lifts to reveal a companionway down to the next deck. A simple rectangular marking on the carpet would mark its location.
I suggested the very same thing in another thread some time ago. As you noted, it wouldn't really need to be functional, just markings to imply its existance (otherwise, the set would need to have been positioned over a "pit" built into the soundstage). Except for the purposes of staging, that empty spot front of the navi-helm station is a bit useless. A "hatch" gives an "in universe" reason for it to be clear.
Sincerely,
Bill