Could the Hafsids not become vassals to the Ottomans much like Crimea did?
Well, it's technically doable, but I don't really see this happening easily : while Crimeans beneficied from good relations with Constantinople (on the matter of trade, for exemple), Tunis clearly didn't have this kind of interests.
It would require a deep strategic shift from support of Italian traders and more western-leaning relations, which could cause a lot of political troubles.
If it's pulled (again, it's not unthinkable, just it would have bad consequences), then Hafsids would certainly go trough a really important decline (more than the one they went trough IOTL) with probable territorial losses and economic irrelevance (safe maybe agricultural production and piracy).
Ottoman control in the region wasn't strong to begin with.
While the bey had important autonomy, it was an important autonomy compared to the vilayets of the Empire. Ottoman influence was objectively quite strong in Tunisia.
Beylerbey, in the early days, were basically men sent directly from Constantinople, which mean strong political power subservient to the Sultan and not local forces (hence why Maghrib was really reunified by Ottomans, from a shitload of de facto independent harbours).
One could argue that the bey managed to get free from direct provincial administration, its very legitimacy went from Constantinople (hence why they "annexed" the pasha function) and Turkish military forces were a political force as well (contrary to what existed in other regions, Jannisaries were Turkish, meaning a lesser relation to local political factions).
Admittedly the whole region becomes a clusterfuck of various interests, but I wouldn't mix large autonomy and factional fights, with "not strong to begin with".