Checking the dialog option's requirements, the likely reason is that Volturn needs to be under Sindrian Diktat control to appear. (And the other two planets to be safe with the rest of the quest, Sindria in particular will be needed for the special fleet spawning)
If someone else has taken Volturn already in Nex, you can flip it back the SetMarketOwner console command
Thanks for mentioning it! I didn't clarify, but 4 planets (Sindria, Cruor, Volturn and some pirate planet, I hope I remember correctly - Umbra) are under SD control, 1 planet under Independent. There weren't any captures/recaptures except for that pirate planet that under SD flag now.
I'll try to experiment with enabling/disabling mods and will post any meaningful results if I'll get them.
edit 1: Ok, SO, this wasn't really expected. I started a new run with the same mods just to test if the quest would work in it, AND IT DID! I've got an accepted mission (I didn't get even mission on the previous after the dialogue) and there's an additional option on the Volturn.
So this may even not be a mod issue.edit 2: Final asnwer... Thanks, Histidine! Umbra should be under pirates control in order for the quest to really start. Resolved!