In many cases people ignore that relationships are two way things... Russian Black Sea Fleet vessels might think of Sev as their home, but I would rather expect that a lot of the Crimea thinks of itself as the home of the Black Sea Fleet too. I rather suspect many of the locals have good relations with Russia and Russians... as shown by the protests when a NATO vessel visits the port.
Perhaps a referendum is in order?
On the one hand you have all the infrastructure and investment in what is basically a foreign country, and of course all the people.
The lease has been extended into 2040, but what happens them?
The Navy is going through a huge rebuilding phase right now, perhaps some hard decisions need to be made... foreign bases are going to become important to Russia including Tartus and Cuba and Venezuela and Vietnam, which in the change of a government could all be lost, which would be a problem but not a reason not to have them.
Perhaps the solution is to move the HQ for the BSF to Novorossijsk, but keep the fleet at Sevastopol.
That would shift thousands of people out of Sev and into Nov, which will shift a lot of spending from the Crimea back to the Russian economy and will enable better information security. It should also add investment to Novorossijsk which should be good for them, and for the Crimea it will likely free up some old buildings.