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No NATO absolutely does not recognise Crimea as being Russian. Not even Russia's big 'ally' China recognises Crimea as being Russian.
No NATO does not need to compromise with Russia over Crimea.
After the failed assault on Kyiv and failing to conquer Ukraine in 3 days the main Russian goal has been securing a land bridge between Russia and Crimea because without said land bridge holding Crimea is absolutely untenable.
Once the land bridge falls its merely a matter of time until Ukraine takes out the new bridge connection and completely isolates Crimea. At which point it becomes utterly impossible to hold.
Russia was able to annex and hold Crimea because Ukraine wasn't ready in 2014 and no one was willing to go to war with Russia over it. Russia itself solved that 'problem' by being renewing the war themselves so now the West can keep supplying Ukraine and give them the means to reclaim all of their territory, including Crimea.