In what episode of TNG is it established that Vulcan ships have no weapons? Any other information on the Vulcan commitment to peacefulness and pacifism are welcome.
You are likely remembering ST:TNG Unification Part 2 from http://www.chakoteya.net/NextGen/207.htm
The Bar Scene with the Ferengi weapons dealer...
RIKER: Commander William Riker, USS Enterprise.
OMAG: Am I supposed to stand up and salute?
RIKER: We're investigating the disappearance of a Vulcan ship.
OMAG: Well you've got the wrong Ferengi. I never trade in Vulcan ships.
RIKER: We know that you're involved.
OMAG: Who would want a Vulcan ship? Vulcans are pacifists. I deal in warships. Can somebody get me a napkin?
RIKER: Who would want a Vulcan ship?
OMAG: Hypothetically speaking?
RIKER: Hypothetically speaking.
OMAG: I never learned to speak hypothetical.
On Vulcan pacifism ST:TOS The Savage Curtain transcript from http://www.chakoteya.net/StarTrek/77.htm
SURAK: In my time on Vulcan, we also faced these same alternatives. We'd suffered devastating wars which nearly destroyed our planet. Another was about to begin. We were torn. But out of our suffering some of us found the discipline to act. We sent emissaries to our opponents to propose peace. The first were killed, but others followed. Ultimately we achieved peace, which has lasted since then.
KIRK: Circumstances were different then, Surak.
SURAK: The face of war has never changed, Captain. Surely it is more logical to heal than kill.
KIRK: I'm afraid that kind of logic doesn't apply here.
SURAK: That is precisely why we should not fight.
KIRK: My ship is at stake.
SURAK: I will not harm others, Captain.
SPOCK: His convictions are most profound in this matter, Captain.
KIRK: So are mine, Spock. If I believed that there was a peaceful way out of this
SURAK: The risk will be mine alone. If I fail, you lose nothing. After all, I'm no warrior.
SPOCK: The captain knows that I have fought at his side before and will do so now, if need be. However, I too, am a Vulcan, bred to peace. Let him attempt it.
KIRK: You saw how treacherously they acted.
SURAK: Oh, yes. But perhaps it's our belief in peace that is actually being tested.
KIRK: I have no authority over you. You may do as you think best.
False they do have weapons. Although classified as science vessels, they can serve as war ships. https://memory-alpha.fandom.com/wiki/Suurok_class