Re: "If Ukraine wants to fight a war with Russia"
Putin had publicly stated that he considered Ukraine to be an integral part of Russia and not an independent country
More importantly:
1. Sevastopol is the only good deep-water port in the eastern Black Sea. Russia has to control Sevastopol if they want to be able to project naval power effectively into the Mediterranean and through the Suez into the Arabian Sea, and on to Africa, India, etc.
2. Controlling Sevastopol requires a friendly nation control Crimea. When Ukraine pivoted toward Western Europe and the USA, it became unfriendly, so the only remaining candidate was Russia itself. (Crimea also contains a bunch of Russian-identifying people, of course, but despite public rhetoric I can't see this being a major factor in Putin's calculus, aside from making holding the peninsula somewhat easier.)
3. Crimea is poor land. Potable water and arable land are in short supply. It has to be supplied from the mainland. Russia's bridge to it was vulnerable, and indeed was successfully bombed. To secure Crimea, Russia needs a land bridge, and the only one is through eastern Ukraine (which also has a lot of Russian-identified inhabitants, but parenthetical from #2 continues to apply).
4. Russia has now made the situation worse for itself, because the war pushed Finland to join NATO. Hostile Nordic countries, particularly Finland, severely imperil Russia's Arctic naval bases and ability to project naval power through the Arctic and the Baltic.
5. Also, polls (to the extent they're reliable) show that Russian citizens overwhelmingly approve of the war, so it's important for shoring up Putin's power and the cult of personality that feeds his ego.
Russia really, really needs Sevastopol if it's going to continue to regard itself as a superpower. Let me be clear – that in no way excuses either the invasion and annexation of Crimea, nor its behavior in the current conflict. But this war is not about Putin's personal beliefs or his tenderheartedness toward ethnic-Russian people living in Crimea and the eastern Ukranian provinces.