Language follows culture and power.
Make Venice a mote dominant power in the Balkans- screw the ottomans and hingarians, mayne go bold and have venice absorb neotheen italy or pull a raj on the mamluks. With that wealth and orestig3 comes soft power comes cultural hegemony comes assimilation.
An Ottoman screw might go poorly for Venice as they were their primary trading partners. Everything from Asia passed through the Ottomans or Mamluks before ending in the hands of Venetian merchants prior to the Portuguese sailing around Africa. Have them suffer instability, and trade might be disrupted and weaken the Venetian position. That said, maybe an early enough screw in which the Ottomans don't take control of lands on the European side of the Bosporus might mean that Venice holds onto its European holdings for more centuries (the loss of Negroponte and Albania in the 15th century, then the Morea, Naxos, Crete, and Cyprus in the later centuries). That might require a stronger Byzantine state that retakes some of its holdings but weak enough that it doesn't retake all of Greece and the Aegean. I am unsure about the relation between the Hungarians and the Venetians- the Hungarians claimed Dalmatia as one of their lands under Croatia but they did not have a war outside of the first one that gave Dalmatia to Venice, so that might not be as relevant (unless the Venetians claim the entire Croatian littoral which they might snag if the Hungarians are especially weak, but the coast does not have many good harbors). It already more or less took control of Northeastern Italy IOTL, with any future expansion butting heads with the Pope, Milan, or the Habsburgs. An outpost in Mamluk lands would be interesting, like a colony in Cyreneica, Syria, or Alexandria, allowing them to bypass the Ottomans if they ever become hostile.
I think you would need Venice to be a more open Imperial Power for a higher degree of a assimilation. Even more than the Spanish in the Americas the Stato da Mar was run for the Metropolis by people from the Metropolis with all the key posts being held exclusively by "native" Venetians. So the carrot for assimilation, greater opportunities, wasn't there while the stick, exclusion from your original community was very strong. Therefore relatively little assimilation.
Would it be possible for Venice to expand further inland, thus necessitating more integration of local populations?
I'm not saying they need to take over too much more territory. Just more hinterland - Slovenia south of the Sava, Primorje-Gorski Kotar County, Lika-Senj County, and more area around the hinterland of Kotor, and Herzegovina seem like plausible expansions to me.
What might cause the Venetians to see assimilation as an important policy to enact and extend privileges to non-Venetians? It appears they were content to simply use their language to run official matters and trade while letting those not involved to follow their native tongue and customs. They did gain a good deal of Terraferma that was non-Venetian speaking: Bergamo and Brescia in the west were both Lombard, and Friuli was, well, Friulian. The coastal areas were Venetified like Monfalcone and Grado, but not the hinterland outside of the areas that were already Venetian like Treviso and Vicenza. If anything, the gaining of more non-Venetian land might simply serve to strengthen their current approach which is to use Venetian as a language of administration and trade, not wanting to irritate the greater number of people they have.
Would they have much reason to gain the listed regions? Littoral Croatia are severely under populated and lacks good harbors; Slovenia/Carniola is a maybe if they take the lands around the Isonzo River like Gorizia but the Sava is too far; it is outside of the Venetian agenda which is to control the Adriatic and Po trade routes. Unless control of the Laybach/Ljubljana trade routes was one of their priorities, they might be fine with simple Gorizia and Trieste. Herzegovina requires they subjugate Ragusa first, then maybe it will be worth the attack; Montenegro and the hinterlands around Kotor were taken IOTL, but a series of wars with the Serbians and later the Ottomans stripped them of it, meaning those would have to be weakened for the Venetians to become overlords of the hinterland.
Define native, Venice did colonize Crete with its citizens to an extent, and some natives spoke Venetian. But most of the rule was either distant or with oppressive colonists. The main reason was that the standard of living within Venice was too high for most to leave, whereas IOTL's colonization was done by "undesirables" that the rulers wanted out anyways.
So just to clarify, Venice wanted to keep as many of its citizens living within the city because most of them were valuable in some way? Or that people simply didn't want to leave because living standards were great in Venice as opposed to its colonies?