A few things get conflated here, and they matter.
You are describing the island, but the Comune of Venice is around the 12th most populous municipality in Italy (roughly 250,000 people). Most of that population does not live on the island at all, it lives on the mainland: Mestre and Marghera are part of the Comune di Venezia too. The 49,000 figure is only the historic centre. So "with its population Venice does not even qualify as medium" is measuring the wrong thing.
The mainland side is not a tourism monoculture. Porto Marghera is one of the country's historic industrial and port districts and there are medium and large firms of national relevance. I work for a medium-sized company in Mestre myself, and my commute from the island is under 10 minutes by car (the island is tiny, and the car parks are easy to reach, especially from a residential neighbourhood).
Venice is not a generic "medium town", so comparing it to one is off. It is a regional capital (of the Veneto), a metropolitan city, a major university and cultural hub, and a port. The public sector here is not "artificial", it is regional and metropolitan government, the port authority, real administrative functions. If you want a fair benchmark, compare it to Florence or Bologna, not to a provincial town where you park on your doorstep.
You do not need a car on the island because the water public transport runs across the whole city all day and through the night, and the place is small enough to cross on foot. For anyone working on the mainland, the parking, the train station and the jobs are minutes away. A car-free historic city is something most cities are now trying to engineer on purpose. It is a feature, not only a trade-off.
And here is the key point that flips your framing: people are not leaving the centre because there are no jobs. They are leaving because owners can make far more converting a flat into a short-term rental than renting it long term, so even someone with a solid job in the metro area cannot find a home in the centre. It is not weak demand for living there, it is demand being outbid by tourism. That is exactly why the lever is housing regulation, not the entry ticket. The university, the culture, the port and the administration already give the city an economic base. What is missing is keeping the homes available to the people who would happily live and work here.