Have I unlocked all the game mechanics?

[Naria]

Assuming you mean all story quests, if you don't do continue through the story quests you will be unable to access jobs and the associated abilities, certain general abilities for treasure hunting and desythesis, glamours, chocobo training, the beastman vendors, the sightseeing log, some emotes, possibly PVP, as well as most of the content of the game. Also there is a fair chance that if you raise a class to 50 with no job you will get mistaken for a RMT by the community, at they tend to be the only ones who completely abandon the story quests, as opposed to just progressing slowly.

[Niwashi]

Assuming you mean all story quests, if you don't do continue through the story quests you will be unable to access jobs and the associated abilities, certain general abilities for treasure hunting and desythesis, glamours, chocobo training, the beastman vendors, the sightseeing log, some emotes, possibly PVP, as well as most of the content of the game.

No, most of that is just level dependent.

The Summoner job is an exception, as that one requires having beaten primals during the main story, but the OP is already far enough in the main story to unlock Summoner since its level 30 quest only relies on the level 20 Ifrit. (Its level 35 quest, however, requires having beaten the level 34 Titan, so by then you need to be pretty well caught up on story quests.) Neither Scholar nor Bard jobs have any such storyline progression requirements. (I'm not certain of others, since those three are the only ones I've unlocked so far, but I think most of them are like Scholar and Bard, where you only need the appropriate levels.)

Nor do treasure hunting, desythesis, chocobo training, sightseeing log, or PVP require anything in the main story beyond the point where you join a Grand Company. (I'm not certain on glamours or the beastman vendors.)

By the time you join a Grand Company, you have all the features the main storyline will grant you up until endgame. (At endgame, though, as several people have mentioned, pretty much all the additional content and questlines require having finished the main story.)