The government will do whatever the clone soldiers want them to do because the clone soldiers will be the government.
As Mao observed in one his breaks from sociopathic mass murder, "political power flows from the barrel of a gun." Governments are at their heart merely instruments for collective violence. The most basic government is a general/warlord and his victorious army. In all times and places, the military decides the form and nature of the government.
I consider the idea of the malicious creation of super-soldiers even on the small scale in "secret" experiments to be one of the stupidist tropes in Science Fiction. You don't give off scale military effectiveness to someone you don't trust and don't deal fairly with because they will kill you.
There are many historical precedents for the scenario you envision. The two most famous would be Malmuks of Egypt and the Janissari of the Ottoman Empire. In both cases, rulers created armies of foreigners, usually starting with slaves.
The Malmuks, were a mishmash of young men of many different subcultures and non-muslims faiths swept up in the Islamic conquest of Christian north Africa and their non-Christian surrounds. With their homes destroyed and the under foreign rule, their families dead, enslaved or scattered, the opportunities offered by a life of slave soldier didn't seem so bad. At least you got to eat.
The Janissary where Christian children from the area of modern Romania, Bulgarian and Balkans taken around the ages of 6-9 as a mandatory tax tithe (hand over your son or we burn your village down.) Christians were taken, as enslaving fellow muslims, well true muslims often defined on the fly, is forbidden by the Koran and the Ottomans didn't want the hassle. When they grew to adulthood they could convert to Islam and "volunteer" to continue serving. But as they had no memory of their families or how to find them again, they had little choice but stay. Telling, the symbol of the Janissary was a large wooden spoon worn on the front of their headgear, a symbol of the Sultan's pledge they would never go hungry. (Food was the major concern of humanity until the Corporate-Industrial-Fossil-Fuel Age.)
The Sultans turned to slave armies first as internal security troops, as a force wholly dependent and loyal to the Sultans and not some noble or clan as were the rest of military. If some noble rebelled, the slave armies put it down. (Its the same reason they relied on eunuchs. Family pull was so strong only someone without testicles and a hope for a descendants could be trusted. Eunuch taken as slave from far away where even better)
Since the slave armies lacked any families or birth status, the only means of promoting them lay in judging merit. Very quickly the officers of slave armies became comprised of individuals who rose by proving themselves in battle. They soon became the most elite units of their respective polities.
As time passed the Sultan became more and more dependent on the elite slave armies. Things worked fine for a century or so but eventually there was some instability in the realm and the slave armies looked around and thought, hey, we don't have to take orders anymore.
In the case of he Malmuks, they merely replaced the ruling class of Egypt and survived until Napoleon crushed them. The Janissary kept the superficial appearance of the Sultan being in charge but were in fact a Praetorian guard who selected who could and could not be Sultan. In both cases, as they came to power, began to marry and form clans, they lost merit promotion and with it military effectiveness.
The moral is that its impossible to politically control highly effective soldiers if they don't want to be controlled since they themselves form the basis of coercive political power of the state.
The form of government is dictated by dispersion of military force in a society. If most of the population is disarmed and only a small elite allowed weapons and training, you have an oppressive, authoritarian regime. If the majority of the population is armed and trained, you get some form of democracy e.g. Athens, Roman Republic, Britain and the U.S.
There are no historical examples of any degree of democracy in societies where the majority of the population is disarmed and conversely, no examples of authoritarian regimes where the majority of the population is armed.
So, the real question in your scenario is not what the "government" will do with the clone army but what the clone army will with the government.
I would also point out that any society which cannot muster enough internal cohesion and form enough political consensus to muster an army from its own population, is dead anyway.
You can see this in history in Carthage, the late Roman empire and Byzantium. Once they could no longer raise a military from their own population, they spiraled down hill. All had plenty of population, they just did not have the internal cohesion and trust to build a military.
So, the fact that your society resorted to a clone army, unless faced with an enemy using super soldiers themselves, would indicate a disintegrating polity.
Even if the society was willing and capable of defending itself without the clone super-soldiers, the clones will still be the de facto rulers of the society once the war ends. They might take over like the Mamaluks, or they might leave the illusion that the old regime is still intact like the Janissary but they will still rule.
You might want to investigate the actual scientific evidence about what makes a good soldier. To much of what we think we know comes from smug, morally self-rightous pseudo-intellectuals who bloviate with based on no empirical evidence.
In the case of industrial warfare, strength is largely irrelevant but low term physical endurance and ability to function with less sleep become more important. Intelligence might be a bonus depending on what you mean by "intelligence." Visual spatial skills are the most important for all types of soldiers from ground pounders to pilots to generals.
The most important qualities for soldiers are emotional, not cognitive.
You'd want to make them calm and hard to excite so they keep aware and thinking as everything explodes around them. Also, give them a touch a ADD to they will be more aware of changes in their environment and not get fixated on one aspect of it.
The most important quality for military effectiveness is unit cohesion i.e. how strongly individuals bond with and trust other soldiers both those immediately around and the greater organization. Highly cohesive militaries have defeated much larger otherwise equivalent militaries repeatedly throughout history.
The second most important quality is a belief in a higher good, something the soldier will love enough to willing die (and kill for.) Both these attributes require that the soldiers have high levels of empathy, something counter-intutive but obvious once you think of it.
You could create "super-soldiers" merely by making clones highly empathetic, cooperative, trusting and then indoctrinate them with an ideal to protect. They would be more effective than ordinary people even with the same IQ and strength.
The problem you might have after the war would be when the clones encounter the real world and find out that the rest of society is cynical about the clones ideals and that far to many civilians lack empathy, won't cooperate and don't trust each other. The clones might be shocked to be lied to or cheated by individuals that they consider part of their group instead of enemy.
The clones might well decide to take over in order to enforce their ideals and ernest behaviors on their imperfect natural brethren.
Regardless, the super-soldiers will decide the outcome and no one else.