TL DR Something is definitely still messed up and not working right, if you don't care about quest/triumphs completed for seal, ignore all and just grab Icebreaker catalyst from the one checkpoint bot. If you're still having issues with the quest legs, exhaust options like looking to see if there is a collectible pickup, soloing up to the puzzles you need, joining checkpoints of people who completed/don't care about the quest and see if anything happens, and if no luck still you might need to grind out a 2nd Icebreaker. You can do Puzzles 1-3 without, but you need to have gotten Icebreaker to do Puzzles 4-6 it won't show without it. Bungie needs to fix this for people still with issues, same for Sundered Doctrine.

Background

For a year and change I've seen a lot of chatter on this quest being stuck but not really that many good solutions or larger understanding of how badly things could be screwed up and I wanted to offer some suggestions for those in need because I am one of those people who had spoke about things being messed up on this sub since basically the Dungeon's launch and only recently had things get fixed through the puzzles 4-6 appearing on a second drop of the exotic. There just isn't really enough good info as to why/how things can be screwed up and it was annoying considering how it wasn't like I didn't have the exotic in the first place . To make matters weirder when I got the very recent second drop of Icebreaker the other week, my game weirdly counted me getting Icebreaker as Recently Discovered for a second time. I am not being forgetful or on a secondary account, I had Icebreaker previously and for whatever reason I got it to pop up again.

As a disclaimer I am only relaying what I have experienced myself and am not claiming this will guarantee be a catch all fix when there have been multiple different issues at different segments reported with this quest line, this could all be very dumb luck, coincidental and might not actually be a fix for everybody(especially if you had multiple drops of Icebreaker with no change). For context I was missing puzzles 4-6 until my 2nd drop of Icebreaker. I do highly highly recommend trying really anything before mindlessly subjecting yourself to farming for a second exotic of all things. Vesper's boss isn't impossible but it does take a particular mood to get into it on grind. I don't really have any answers for what happens if you can't even get puzzle 1 or 2 to show and have done all the steps prior.

You cannot get puzzles 4-6 to show if you never got Icebreaker at all despite how the game lets you do 1-3 without it. I also would recommend entering the dungeon solo when you go looking for missing puzzles and do not invite anybody who's ahead of you or completed things. You could try to hop into somebody else's original lead checkpoints at each of the stations, but it isn't necessarily a guarantee anything you need will show.

You technically only really "need" Rogue Network completed for the 6 puzzle messages for the Title/Seal for Vesper. If you really don't care about the title/seal, a specific checkpoint bot still exists for giving out the Icebreaker catalyst checkpoint state and you can ignore everything in this post. You also can have somebody who completed everything punch you in the code for the class item for the Trophies of Vesper triumph component as well.

Cause of Issues

One of the biggest issues with this quest pathing and not having puzzles showing up is likely a result of somebody in your fireteam who was on quest steps ahead of you, doing puzzles you weren't on and the game somehow counts you in some way as having completed that segment. I have a feeling this is why Bungie kept saying in TWABs "just pick up the message, it should be there", yet they don't understand there are various situations when the message just won't render to be picked up, or you do see a prompt but there is no physical thing to grab and the message doesn't count, and you're stuck.

There has been plenty of chatter of fixes such as doing Vesper with somebody who has never done it before or somebody on a different puzzle sets' steps, but unfortunately these can lead to situations where you might have your missing puzzles finally show(which obviously good) but you're now the one to screw over somebody who's now going to be the one with issues. This entire thing is super finicky with account history in the dungeon, and I have a feeling that the game pretty much takes whoever's completed the most/finished into consideration even if they haven't lead and it screws with stuff. You might get weird results in a fire team of people all on different progress and who specifically was lead to load in.

My Experience I had somebody in my fireteam when I was on either my first or second run(no progress in the quest) do Puzzle #3 and this lead to a situation that Puzzle 3(and the message pickup) was absent and it only showed up until I basically solo loaded into Vesper and wiped at every single instancing checkpoint area until right before it. This location in Castor Complex right before Raneiks I feel has a very particular instancing point and wiping here and going to orbit was where I felt like things "fixed itself" for making Puzzle 3 show, you again might need to keep wiping at each possible instance change.

After this somebody in a different run of Vesper did Puzzle 4 when I wasn't on it and thus I was locked out on Puzzle 4-6. By this point I had gotten Icebreaker to drop so it didn't really make sense why I just could never get it. I did literally everything I mentioned above and no luck. Hell I even screwed over somebody in a similar fashion when I loaded into their first run of Vesper, and they had nothing show. Though I do wonder if the alleged EoF fixes people talk about mean you can't ruin things for others, I honestly hadn't tried to do a repeat in recent time. I also had a situation when I finished Puzzle 5, lost my jump mid air when trying to clear the gap to dunk Operator and it wiped me BUT I was able to pick up the collectible Message 5 when I went to its location, however Puzzle 5's Scan/Operator buffs completely disappeared after that. Puzzle 4 I could still see plain as day once I completed it which I thought was weird. Be mindful of this you very well could have a collectible you could grab and no puzzle showing.

Possible theory

While I'm not ruling out just a lot of stuff just not working right and nothing makes sense, I do wonder if another part of this is some sort of technical deeper level thing that has to do with how the game interprets ownership of Icebreaker in regards to the Puzzle 4-6 steps and perhaps specifically to which character got the exotic and who did the puzzles. I know Finality's stuff was best keeping to 1 character doing the quest progress to prevent screwups despite how once you do it fully, your 2nd and 3rd char can auto have the max level access without doing the quest over again. I keep bringing up the 4-6 segment because I had a clanmate who had Puzzles 1-3 completed without Icebreaker, 4-6 never showed up until they eventually got it for the first time. Not saying this would be the weirdest thing ever, but considering how Finality Auger catalyst quest let you do the entirety of it without having the exotic and the actual stuff you really do need Icebreaker for happens once Rogue Network is technically over, I feel like it shouldn't have been such an issue. I would recommend if you're starting the quest from scratch keep all progress to 1 guy.

If you're somebody who's still having issues I'd love to know what you have tried, how you got stuck, did anything suddenly start working like the experiences I had for to unstuck 3? I feel like there needs to be more organized info of what people have had work and not work.