I suspect they will maintain a force of dreadnoughts. They have no real need to operate beyond the Med, so any capital ships they build will most likely be small, with a rather short range, as the war showed that they did not need that much of an operational range, bottled up in the Adriatic as they were.
Immediately post-war, the navy will be downsizing as part of the austerity program to pay off the debts incurred during the war. I expect that older ships will be decomissioned and scrapped. This includes the Habsburg and Erzherzog Karl pre-dreadnought ships (6 vessels) as well as the Kronprinz Erzherzog Rudolf and the Wien class.
Before the war, Austria-Hungary had the ambition to have 2 squadrons of 4 dreadnoughts each, supported by older ships. I believe this will be reduced to 2 squadrons of 3 ships and no supporting older ships, as, conveniently, both the Tegetthoff and Radetzky classes now consist of 3 ships.
Furthermore, the older protected cruisers will be scrapped and replaced, along with the older light cruisers. The Austro-Hungarian navy will probably aim to have a small fleet of heavy ships and a larger one of torpedo boats/destroyers with small but fast and powerful light cruisers/destroyer leaders to stiffen them up and conduct recoinnassance.
So, 1922, the navy looks like this:
3 dreadnoughts (SMS Viribus Unitis, SMS Prinz Eugen, SMS Tegetthoff).
3 semi-dreadnoughts (SMS Erzherzog Franz Ferdinand, SMS Radetzky, SMS Zrinyi).
4 light cruisers (SMS Admiral Spaun, SMS Helgoland, SMS Novara, SMS Saida).
16 destroyers (Tatra, Wara Sdiner and Ersatz Tatra classes - 10 surviving ww1, 6 built afterwards).
At that time, some new construction will start to happen. Austria-Hungary will probably accept parity with the Italians during the Washington treaty negotiations, and will probably stick to their part of the deal, and perhaps even have less than that.
The Tegetthoff class will be upgraded and updated during the 10 year "holiday", say 1928-30, one ship at the time. New shells for the main battery allowing for a longer range, perhaps modficiations to allow greater elevation too. The secondary artillery will be taken out and new 15cm turreted guns (6x2x15cm) installed, 3 dual turrets on each side. The 6,6cm guns will be taken out and replaced with 6x7,5cm AA guns and 8x20mm Bekker autocannons to fight planes and MTBs. The boilers will be replaced with oil fired ones and the bows replaced to more modern cruiser bows (instead of the heavy ramming bows previously installed). New range finders will be installed, and a new and modren fire control room will be created in the deepest part of the ship when the torpedo tubes are ripped out as unneccesary. A new mast will be installed as well. The tonnage is actually reduced somewhat, as the bunkrage is reduced and the heavy bow taken away, and the combination of engine overhaul, new bow and slightly lighter load increases speed to some 22 knots.
The 3 semi-dreadnoughts will be replaced by 3 new constructions once the 10 year "holiday" of the Washingtong treaty is over. These will be small but heavily armed and armoured dreadnoughts capable of good speed and oil firing. The crew comforts and bunker abilities will be rather low, and they'll have short range as they'll be expected to dominate the Adriatic against the Italians. The Italians only have ships with 30,5cm" main batteries at this time, and their 38cm ships were not laid down until 1934, so I am inclined to think that the Austro-Hungarians will stick with what they know - 4x3x30,5cm guns. This has the advantage of them using all their battleships at the same time with the same range, same guns and the same shells. The ships will be 25-30 000 tons, carry good armour and might have 4x3x15cm dual-purpose secondary artillery (Skoda did design dual purpose field artillery and sold it to Yugoslavia in the 1920s OTL) and a speed around 28 knots and being oil fired.
One of the older semi-dreadnoughts becomes a sea plane tended and another an accomodation ship.
By the time ww2 rolls around, if it does, Austria-Hungary might be looking to replacing the modernised Tegetthoff class, probably with something with a 38cm main battery to counter the newer Italian ships.
When it comes to cruisers, I expect the Austro-Hungarians to interpret their experiences from ww1 in a sense that they need 2 larger light cruisers, to fly their flag over the world, represent them in hotspots and protect any merchant ships (or do merchant raiding) they may have around the world. These will probably be laid down around 1924-25 and be armed with 4x2x15cm guns in turrets and include 2x4x53cm torpedo tubes, do 32-34 knots, displacing just short of the 10 000 tons of the Washington naval treaty.
The other light cruisers will be smaller, probably around 6-8 000 tons, probably number 6 (one each as a destroyer leader to head the escorting flotilla of each battleship) and carry about the same armament and performance as the larger cruisers, only with a shorter range. The Austro-Hungarians will probably watch Italian cruiser development closely and aim to have their ships be capable of 1-2 knots more than their Italian equilents, in order to be able to quickly attack, raid and retreat in any Otranto blockade-like situation. I expect that by 1939, they actually have 9 cruisers as they have built 3 more modern ones (to counter the Italian Condottieri class) but not scrapped the older ones built in the 1920s.
In addition to this, the Austro-Hungarian navy aims to have 54 destroyers (3 groups of 3 for each cruiser/battleship to lead), of which 6 will be larger destroyer leaders. The destroyer leaders will do 40-42 knots and be armed with 2x2x15cm, same guns as carried by the cruisers and dispace 2 000 tons or more and be similar to the French Le Fantasque class while the regular destroyers will probably be around 1 200 tons and carry 4x1x12cm guns.
I expect one or two of the older cruisers to be converted into a mining ship and the Austro-Hungarian navy to have a large fleet of small minelayers and minesweepers and a strong fleet of submarines focused on merchant raiding.
I don't expcet any carriers, but sea planes aboard the ships will probably be common configurations until radar is commonplace.
