Guarantees "complete freedom" of passage for all civilian vessels in times of peace. In peacetime, military vessels are limited in number, tonnage and weaponry, with specific provisions governing their mode of entry and duration of stay. If they want to pass through the Strait, warships must provide advance notification to the Turkish authorities, which, in turn, must inform the parties to the convention.
In wartime, if Turkey is not involved in the conflict, warships of the nations at war may not pass through the Straits, except when returning to their base.
When Turkey is at war, or feels threatened by a war, it may take any decision about the passage of warships as it sees fit.

Montreux Convention signatories who are also allies of Ukraine are not at this point active belligerents in the Ukrainian war, so technically, it would be 100% above board for any of them to send a military vessel into the Black Sea.

Incidentally, the US is not a signatory to the Convention.