If we're strictly speaking on the US side about the CIA program (and not other torture like Abu Ghraib etc.--conducted by the military) the answer is that
Obama decided not to prosecute anyone who followed orders, or officials who approved the policy [...]
[Obama] worried that investigations could be viewed as a "partisan witch hunt." Once he took office, [...] Obama quickly decided not to even open cases against either officials who followed Bush administration "rules" on torture or the officials who wrote those rules in the first place. [...] And his new CIA director Leon Panetta quickly vociferously argued for no new investigations of the agency. [...]
Attorney General Eric Holder released his own statement in April 2009, saying, "It would be unfair to prosecute dedicated men and women working to protect America for conduct that was sanctioned in advance by the Justice Department."
However, the possibility of prosecuting government officials who had gone further was deliberately left open.
But then Holder decided not to prosecute any cases where officials went beyond the approved techniques.
It looked at first like some of the officials in these cases might be punished. In August 2009, Holder announced that he was specially appointing a prosecutor, John Durham, to investigate the agency's interrogations.
But after a two-year review examining conduct of the CIA regarding 101 detainees, Holder and Durham decided to focus on just two cases in which suspects held by the CIA had died: Gul Rahman and Manadel al-Jamadi. Further examination of any "remaining matters" was "not warranted," Holder said.
A year later, even those two cases were dropped because "the admissible evidence would not be sufficient to obtain and sustain a conviction beyond a reasonable doubt," according to Holder.
And since prosecutions of this kind need to started by the DOJ rather than by federal courts as you assumed in your Q... nothing [else] happened.
There was one CIA contractor (Passaro) who was prosecuted under Bush for "for his involvement in a detainee's death".
The statute of limitations on certain federal torture offenses is eight years
which precluded charges much later on.
And yeah, Trump said
on the 2016 campaign trail he'd “bring back waterboarding,” so if you [somehow] expected his administration to prosecute Bush & co for that...)
Aside here, since another answer mentioned the somewhat related Italy (Abu Omar) case: prosecutors in Italy can't be instantly dismissed by the government, unlike [federal ones] in the US. "Since the adoption of the Constitution in 1948, however, prosecutors have belonged to the judiciary and are guaranteed the same independence and tenure as judges both being classified as "magistrati"". That's why it was possible for that case to proceed even though the Italian government at the time disapproved.
Finally, it's been mentioned in that first piece, but also much more extensively e.g. by Amnesty that countries that claim universal jurisdiction could easily charge some of those US leaders you mentioned (Bush, Cheney etc.) for e.g. violating UNCAT (and not just the Geneva conventions). Wikipedia does mention that
Bush cancelled his  trip to Switzerland after news of the planned prosecution came to light.
Actually, it seems that case might have been more imagined than real: "the cancellation stemmed from concerns about protests, not fear of arrest", according to Politifact. But yeah, even opening a preliminary investigation was not possible under Swiss law until Bush stepped into that country.
It's rather more difficult to give a non-speculative answer why such prosecutions didn't happen [more broadly], but surely it has something to do with US power and influence abroad. Wikipedia also mentions e.g. that a similar attempt in Canada, started as private prosecution under § 269.1 of the [Canadian] Criminal Code, was dropped at the intervention of government's prosecution there (possible under the Canadian procedure code).
Likewise, the Spanish legislature appears to have deliberately changed some of their universal jurisdiction provisions in order to hinder the prosecution of the "Bush Six" in their country. In that case some US senators openly warned the Spaniards that
the prosecutions would neither be understood nor accepted in the U.S. and would have an enormous impact on the bilateral relationship.
Finally, I suspect that the mood in Europe changed even more against such legal actions [against Bush-era officials] after the rise of ISIS, particularly after it conducted attacks on European soil. Cooperation with the US against the new Islamic terror probably became much, much more important. (In particular because the US intervention in Syria was hardly uncontroversial from an international law perspective, and the alternative for Europe would have been to go hat-in-hand to Putin and Assad.)
But, as a kind of coda to this story on the European side, since a number of rendition and torture targets/victims were able to bring suits in European [national] courts for the cooperation of such goverments with the Bush era events, and since they generally lost a bunch of such cases in [European] national courts, the ECHR ended up hearing a number of rendition-related cases around 2012-2019. However, such cases are esentially the US equivalent of civil-rights violations lawsuits [rather than criminal cases], so these gave monetary awards to the victims. E.g. Italy lost an ECHR case related to Abu Omar, Poland lost two related cases involving Guantanamo detainees, Macedonia also lost one, as did Romania and Lithuania, and I don't claim this is a complete list.