IIRC, you mentioned this back then in the discord; will post here as well, just in case someone else has the same misfortune.
You sent a chat message the exact moment this dialogue popped up - the collision of those two events lead to that horrible "dialogue box freeze" bug.
This is a whole "family" of dangerous bugs in EP4 quests involving popup dialogues. Another good example are those popups of the "x seconds gained!" fashion in NMUx quests. I am (as of now) unsure if this happens in other episodes as well, however it definitely does with the "intrusive" popup dialogue boxes used in a variety of EP4 quests.
After persistent reproduction, i found some dirty tricks to be used as a bandaid/workaround for as long as these bugs persist. Only one of them seems realistic:
• Have someone in your party, whose guild card you have not yet obtained, send it to you.
Explanation: The prompt to accept or refrain from accepting the card will "magically" re-enable input - the frozen dialogue box "thaws". If you are playing pubs with "random" people, it's likely you do not possess everyone's card to begin with. However, it should be communicated before quest start (since habit dictates that people who suddenly stop moving are probably just d/c'd). Woe to those of us who are maxed out on GCs!
This might or might not work with sending team invites, as well.
Establishing the fact that a simple prompt re-enables input, it only makes sense to search for other possibilities in the same vein. There are other, less feasible ways to deal with the problem - however most of them require comparatively esoteric setups and thus are less realistic in field work:
• Have another player KO your character using /pk command while not holding scapes and not being revived. Wait for the P2 prompt.
The big hook? PK mode needs to be activated before the bug happens, which means having to play the whole quest like this. A notably feasible situation would be, if someone were multiclienting with a passive character out of combat reach (ex. passive FO used for S/D only). However unlikely it is for this bug to happen at all when playing alone, imo it is still worth the anecdote.
• Lure any enemy to a frozen character, then distance yourself quickly in order for the enemy to shift their aggro & kill the player. Wait for the P2 prompt.
EP4 enemies coupled with episode design tend to be more stalky than their predecessors in general. Lizards and Astarks for example with their big aggro range will happily follow you outside of their spawn "rooms", and they are not shy about crossing bridges either. Therefore, it is entirely possible to lead an enemy of the next respective room back to the position of the frozen player. The hook here, is that the workaround's possibility is tied to the presence or absence of monsters in the same area (which rules this one out for the boss room, sadly).
One, most likely the ideal solution to this, would be to change the type of dialogue boxes used to "nonintrusive" ones where input is not disabled etc. In my honest opinion, that would be an honorable exception to the mentality of not messing with vanilla.
Another way would be to implement a new command that does nothing else than popping up a prompt to player x (gem color, ex. "/prompt red"). To give broader sense to the whole thing, it could be some dice roll command (ex. "/dice red").
Makes one wonder if the bug can also happen after TTF Falz.. Fortunately, most people just mindlessly spam confirm button after the cutscene lol.