Or, the 'intermix chamber' from the refit 1701 really was
the reactor, having it exposed it for regular repairs was a necessary part of the radical redesign, and so radsuits were sometimes
necessary wear when it was in operation, as in TMP several engineers don't bother from time to time, whereas in the wrecked TWOK situation I don't recall an engineer without one, I don't believe we saw any radsuit at all in TFF (given what we saw of engineering initially of the A was the redressed Jefferies tube) and by TUC only some engineers wear them.
By the TNG-era, the technology had been refined to the point where radsuits were no longer necessary at all and you could quite readily walk up and lay your hand on the reactor.
As for TOS? Obviously, it's reactor was well protected by mesh radiation shielding, so no radsuits there!
I still like my inverted 'V-12' TOS warp reactor.