Austria probably could have gotten by with benevolent neutrality but they came off badly by allying with France (but not doing enough) and angering Russia.
if they joined on the Russian side they’d be knocked out pretty quickly. Could see a bombardment of Trieste and an offensive in Lombardy—which they lose in the peace.
Well, with the main Franco-British effort on the land and sea being against Russia, I don't see how exactly would they be able to spare any significant force against Austria. It is also not quite clear if at that time Piedmont would be able to kick the Austrians out of Lombardy on its own: in OTL during the 2nd Italian War of Independence there were 128,000 French troops and only 56,000 Sardinians against 198,000 Austrians. So Piedmont is hardly in a good position to start a new war in Italy and definitely not in a position to send troops to the Crimea (not that they played any significant role other than as a moral factor).
Austrian friendly neutrality would mean that there is no
Crimean War: Russian troops are not forced to evacuate the Principalities and the Allies are needed to stop their further advance into Bulgaria and beyond at a risk that otherwise their contingents could be cut off from the Straits or at least their base at Varna is in a very realistic danger. Not to mention that at any point more Russian troops could be moved to the Crimea (even with the OTL lousy logistics this was possible).
Austrian direct participation on the Russian side makes things much worse for the allies because the Ottoman defenses on the Balkans are going to crumble well before the French and Brits manage to bring any significant forces to the theater. Probably the allies would have to concentrate on defending the Straits and some raiding operations on the Black Sea.
As far as bombarding any major port is involved, its efficiency depends upon the coastal defenses. In OTL the allies managed to burn some port installations in almost undefended Odessa (6 batteries with 40 obsolete guns) and to take two isolated coastal fortifications, unfinished fort on Aland islands and obsolete fort of Kinburn without heavy artillery but a following attempt to attack Nikolaev failed. During 3 days of attack on Sveaborg the allies fired more than 20,000 shots killing and wounding less than 200 and putting some wooden buildings on fire but not doing any significant damage to the fortifications (of course, Dundas sent overly optimistic report in a reasonable expectation that nobody is going to check it
). In other words, a naval attack on Trieste would produce some results only if the port did not have adequate defenses.