Strictly speaking, the Tactical role is fulfilled by whomever is stood at that station, which has been shown to most often be the Chief of Security in TNG and Voyager (on DS9, the Defiant bridge crew varies a lot, and the Defiant has two Tactical stations anyway), when they aren’t busy with other duties.
TOS-era, weapons are commonly operated by helm or navigation. Enterprise-era, there’s a separate Armory Officer who handles shipboard weapons, with shipboard security handled in part by a MACO contingent (who, obviously, have no presence on the bridge).
Supporting Characters do not have a character role, barring Admiralty-level play (where any officer on any subordinate vessel could be a supporting character). The emphasis is on the player characters as captain and senior staff, and a supporting character in one of those roles (such as the Chief Engineer in season 1 of TNG) isn’t part of that group, so they can get the job title but not the benefit.
That’s pretty much how I view the Operations Manager–it’s whatever (usually Engineering department) officer is at that station rather than being a department head role (I see the Operations Manager as being subordinate to the Chief of Engineering).
Worf was Tactical Officer of the Enterprise as a red shirt until Yar was killed and he took over for Security. It’s odd that he’d wear a Command uniform in a position that you’d expect to fall under Operations, but he was Geordi’s backup at the Conn so maybe that’s why.
That does seem to reinforce that the Tactical role on the bridge isn’t a formal position though. In our game I volunteered to have my character do it, since he’s the XO and on our ship’s small bridge (it’s a Miranda) that position has no dedicated place. And I put a lot into Security so he has the skill to do it. We don’t have a main character as Chief of Security or they might have done it.
Worf in season 1 of TNG was a relief bridge officer - that is, he was essentially a named version of one of the random extras who hangs around on the bridge and mans the Conn, Ops, or Tactical stations as needed (when someone vacates their position).