Austria is knocked out easily when a front is opened in Lombardy and maybe to be extra punitive the RN bombards Trieste.
This assumes that the French are completely re-oriented in their goal in a war and have to abandon support of the Ottomans. Aka, the Crimean War is not happening and Nicholas is winning "by default" by having to fight just the Ottomans with a good chance of a victory regardless unsuccessful OTL operations on Bulgarian border. The open question is about specifics of Austrian involvement and what Austria is trying to get out of the alliance with Russia.
If the agreed upon scenario is Austria getting Walachia (and whatever else on the Balkans) while Russia is getting Moldavia and whatever it can grab in Caucasus region then Austria may reasonably limit its military involvement on the Balkans by strengthening its Italian theater. If it really had 280K in the Principalities in 1954 and Russians had around 120K there against something like 100K Ottomans then Austrians could easily move at least 3/4 of their force to strengthen their position in Italy ending most probably with noticeably more than 198K they did have in 1859.
Potential loss in Italy (
which happen in OTL 5 years later without destroying Austria as unitary monarchy) is being compensated, at least superficially, by the acquisitions on the Balkans.
OTOH, the major French involvement in Italy 5 years ahead of the schedule pretty much dooms its involvement on the Ottoman side delivering a serious blow to the international ambitions of Napoleon III and displeasing a Catholic party in France (control of the "holy places" remains in the Russian hands, etc.). On its own Britain can't do too much on land so the
Crimean war is not happening especially if there are joined Austro-Russian operations on the Balkans with the allied armies marching toward Istanbul as happened (with just Russian armies) in 1828 - 29 and will happen in 1877 - 78. Ottomans are losing parts of their territory with the Franco-British naval force perhaps acting as a "moral factor" helping to make a peace without a loss of Istanbul.
Austria was in a delicate position of course. But couldn’t they have gotten away with strict neutrality or even benevolent neutrality toward Russia? Wouldn’t the Russians have understood this? Was it not the mobilization and threats on behalf of the allies that truly was the last straw for Russia? And of course said actions also failed to satisfy the Allies.
Austrian neutrality means:
Continued Russian occupation the Danube Principalities with a possible invasion of Bulgaria. In OTL Paskevich ordered retreat from the Principalities due to the Austrian position. The Principalities were occupied by Austria for the duration of war and Russian army of at least 120K remained on the border. With Austrian threat gone it is reasonable to assume that the Russians could continue advance into Bulgaria which, depending upon timing, could make allied landing in Varna unlikely or impossible: in OTL the Russian troops crossed the Danube and started siege of Silistria in March of 1854, their removal from the Principalities happened in the end of June and Franco-British troops landed in Varna in July of 1854. Without "Austrian factor" and with a minimal luck by July the Russians could either took Varna or to be too close to make allied landing very risky. Also, with the advancing Russian army of 120K already in Bulgaria the Crimean operation would be a risky enterprise because a successful Russian advance toward the Straits could leave the Allied force trapped and cut from supply lines. As a result, the most probable Allied strategy would be to join the Ottoman army in Bulgaria (approximately 100K), push the Russians back across the Danube (perhaps further, taking into an account the sorry state of the Russian army of that time, this was quite possible) and limit activities on the Black Sea to the raiding and bombardment of the ports. With the bulk of the allied land forces being deployed on that theater, the landing operations look unlikely (but not impossible, especially on a limited scale).