I would find it unlikely Ukraine would attempt to invade Russian held areas of Crimea during the current stage of this offensive. There are limited options for Ukrainian forces to enter Crimea, they would concentrate in two the bottlenecks and suffer heavy losses through concentrated Russian artillery and rocket attacks.

What I would find more likely is the forces push through the landbridge supplying Crimea and then launching attacks against the Kerch Bridge cutting off supplies from Russia. Since they have already hit the Chongar Bridge, they will now likely target the pontoon bridge set up by the Russians. Likewise, there is the road route [the long way round] that could allow Ukrainian artillery to target Russian supply convoys as they take the roads from Armiansk.

Ukraine will soon have long range missiles capable of striking the Kerch Bridge, this is especially so if they are able to push deep into Russian held territory. The French/British designed Storm Shadow missile has a 450 kilometers range and can be launched by an aircraft that could theoretically strike the Kerch Bridge. That puts aircraft at risk of the S-300 and S-400 anti-aircraft batteries so I don’t think they will risk these aircraft just yet, they will push down and take control of ground that they can defend where they can launch air-to-ground long-range missiles.

I would expect Ukraine to wait until they receive shipment of the MGM-140 ATACMS [Army Tactical Missile System] with a 300 kilometer range. I would expect as Ukraine takes ground and pushes towards Melitopol and Mariupol their longer range missiles can come into play. The US has been hesitant to supply Ukraine with longer range weapons. However, the Ukrainian leadership has been careful to not strike targets in Russia with US and NATO supplied weapons.

Not every HIMARS launch system needs to be equipped with the MGM-140 missiles, they really need one battery that can launch six long range missiles towards the Kerch Bridge. From what I can tell, Ukraine does not want to waste lives [I am hoping] to take Crimea, they are likely to create a siege and cut off supply until Russian support wanes. Ukraine may keep the Kerch Bridge open to allows Russians to escape from Crimea and back to Russia but that also allows resupply so I will be watching on with interest what the Ukrainian military leadership will do.