AHC: How far into the 20th Century can you keep the Hapsburg Monarchy going?

Is there any way Austria-Hungary (or Austria-Hungary-Croatia) could survive to the present?
Either avoid WW1 (quiet difficult) or CPs win the Great War (ratherly relatively soon). Then you might be able to reform their empire and keep that around to this day.
It's not easy to keep Austria-Hungary going considering how the Empire collapsed in the aftermath of World War I. Maybe the monarchy becomes extremely decentralized and and symbolic not wielding any real power.

Though the Hapsburg Dynasty may outlive The Austro-Hungarian state. In the aftermath of World War I though the Empire was broken up there was a somewhat active movement in Hungary to place Charles Hapsburg back on the throne. Though a restoration may well have meant war they couldn't win with the Little Entente and an antagonistic relationship with Austria due to border disputes.
To clarify, are you asking for a surviving Austria-Hungary (or a reformed version thereof) under Habsburg rule? Or just that by the modern day the Habsburgs are reigning somewhere on Earth? The latter is easier than the former, but the former is still rather easy IMO. Austria-Hungary was a far more durable state than people give it credit for, and absent either the Great War entirely or a CP defeat after a grueling 4 years of turmoil I see no reason why it couldn't survive to the modern day, albeit changed significantly from its structure in 1914. Even assuming it still somehow collapses after a CP victory, that would still leave the Habsburgs ruling the crowns of Austria and Hungary (and possibly Poland if it gained independence), they'd just no longer be unified as a single entity.
Habsburg monarchy can continue even for the time being if it is reformed

Franz Josef's early death can help

(The shock of the death of his beloved wife devastated him enough for him to fall dead in 1900)

Franz Ferdinand will become emperor

Among the Habsburgs, he was the only one with the correct ideas of the Reformation

I realize that the current situation cannot continue and must be fixed

If he rules until 1914, it will be long enough for him to pre-empt a galactic coup to crush the foolish Hungarian elite.

And try any possible reform to reform the empire and reform the army and navy

In terms of foreign policy, he wanted to restore relations with Russia and was in favor of the status quo in the Balkans

He wanted to return Bosnia to the Ottomans

He hated Italy a lot, so the probability of Austria entering the Italian-Turkish war in favor of the Ottoman side is very high (if it happens).

Or an Italian-Austrian war without the Ottomans?

He may take Italy's colonies in order to sell them to make money

(Eritrea sells to Belgium and Somalia to Germany or gives it to the Dervish State, an ally of the Ottomans)

Or create an Austrian colonial empire

(He buys the remaining Spanish colonies and presents himself as an acceptable alternative to France and Germany as a colonizer of Morocco)

(or to include Austria in any German plans to divide Portugal's colonial possessions)

(Or the capture of Libya during the reign of Abdul Hamid II)

If his assassination continues to happen, even Russia will abandon Serbia to their fate

(Russia hardly tolerated the murder of Obrenovich, though they were Austrian puppets. The murder of the seated Emperor of Austria by the same country is completely unacceptable to the Russians.)

But World War I is still inevitable, but Austria may be neutral

It might take over the German colonies if they joined against the Germans if the Austrians were not the cause of the war
There was this moment in 1917, The government reestablish the Parlament and the Reichsrat who was disbanded in 1914.

On this 1917 Austria-Hungary Reichsrat meeting, the delegate declared there wishes for own independent National states !
Empore Karl I. try to defuse the situation by proposing the transformation Austria-Hungary Real Union into Confederation,
but sadly the Hungarian government under Wekerle miss understood the situation utterly.
Sandor Wekerle rejected the Imperial proposal and demanded a Personal union between Austria and Hungary, what replace the current Real Union
but the „Magyars“ fraction in Hungary Parlament opposed any form of Union, demanding Hungary own independents.
Also express in Hungary living Slovaks, Rumanians and Croats, there dislike about suzerainty of Hungarian authorities over them.

From here it went fast, next the Czechs and Slovak declared there Independence from Austria-Hungary,
Then Polish Galicia declaring to join the kingdom of Poland, that had German establish after Treaty of Brest-Litowsk in 1917.
This with blessing of Germany foreign office and without consulting the Austria-Hungarian government.
Because German Empire politicians consider now the Austria-Hungarian as lost cause

Hungary nullified the Real union with Austria, while the oppress Slovaks, Rumanians and Croats started a uprise in Hungary.
While Sudeten German declared not to be part of this Czechs-Sloavk nation and wanted be part of German Empire,
The German speaking rump state of Austria-Hungary united them self under Nation of Deutsch-Österreich,
it got worst in kingdom of Hungary, that had revolution, were Communist took over part of kingdom.

Had Sandor Wekerle better understand the proposal Austria-Hungary had became a Confederation
we're the Emperor would be head of state of members states.
But still is question of Treaty of Versailles and punishment for A-H since they start the War
in case of Victorious Germany two option are possible:
one the A-H Confederation or if that failed the Germans install Empore Karl I. as King of Hungary
since German Austrian already declare the Republic and offer the wish to join Germany.
Even without substantial structural reform, Austria-Hungary could have survived to modern day. Ofcourse some kind of of reform was likely to take place at one point, but that was not necessarily a condition of survival. The only thing that can bring down a modern state is either another state or prolonged excessive economic hardships.
Is a surviving monarchy possible? Yes, certainly.

Is a surviving Austria-Hungary possible? Not as certain. The problem in a nutshell is: If you federalize the Empire, Hungary will leave. And if you don't federalize, the minorities in the Hungarian part will revolt.

I think the easiest way would be a federalization with Hungary leaving with it's majority Hungarian territories. The Habsburgs would still rule over a nation bigger than modern day Austria.
Austria-Hungary was, in a way, ahead of its time but regretfully out of sync with Europe’s prevailing nationalistic Twentieth Century trend .

But, if this multinational Empire (comprising at least 9 or 10 different nationalities depending on how you count) could have successfully reformed and given all its citizens basic equality, it would be a forerunner of today’s European Union which consists of 27 sovereign states, as of 2022.

In many ways, the European Union offers its citizens a better life and many more opportunities by acting together than if each one was totally separate and competing with its neighbors. Austria-Hungary was already a cohesive economic unit. No reason why some attempt at a better political conciliation could not have at least been attempted.

Instead, after World War One, the Successor States became unreformed mini-Austria-Hungaries and none of them, including the Czechs, gave their minorities full, equal rights.
I think Franz Ferdinand's United States of Greater Austria might be a start, but you first have to make sure Franz Ferdinand lives long enough to see it through
Friendly Reminder that was never FF plans, in fact he never liked it at all once he got the idea as never solved the issue of the Empire and just give minorities pre divided lands to enemies paid agitators. FF plan was more soft power, breaking the power of hungary and trying to have more centralization, not less, so Austria could live up the whole potential, FF did was taking ideas how USA easily keep a nationwide structure under a national language even with migration. FF true plan was to streght the empire as a whole, thing like minorities language were a bugger for him.