Frame challenge: "US backed" is extremely vague, i.e. covers a large range of activities.
Nowadays the US [State Department] will verbally 'back up' any regime that transitions to democracy (e.g. from a military coup). And the Western MSM press will typically applaud a democratic transition as well.
The actual degree of "backup" or rather support that the transition received can vary widely though. From the more concrete support that they e.g. gave the Serbian opposition to Milosevic to nothing more than words.
As for backing up transitions to non-democratic forms, those were surely more common during the [previous] Cold War, when some degree of anti-communism was generally enough for a coup to receive some level of approval, as long as those replaced were perceived to be worse on that angle. Or even just in orientation towards some settlement that the US approved, e.g. improved relations between some country and Israel.
Even then/so, backing up dictators abroad was not without some domestic blowback, sometimes even at Congressional level (e.g. 'Kennedy Amendment' of 1976), i.e. it was fodder for potential 'political football'.
Islamists have sometimes replaced communists as the scarecrow in some contexts nowadays, at least in some part of the world, for US policy decision making.
Also, focusing on support just on the initial takeover event may or may not be too myopic, as aid sometimes is spread over time.
As you mentioned Bangladesh (in new edits)... conversely, lack of much financial support tends to indicate not much backing. E.g. when general Ershad visited the US (in 1983) soon after his (1982) coup, the CIA advised the presidency (in a now declassified, but then secret memo) that "Ershad tends to overestimate the importance of Bangladesh to the United States" and "Ultimately, Bangladesh plays a relatively minor role in US policy", and that Ershad was visiting to seek more aid & private investments, and so boost his domestic standing, particularly in the eyes of the military. It's not hard to read between the lines that the CIA was thus advising "don't spend much on him", which they also phrase as that might be grating India's "sphere of influence" (my term): "Overcommitment of US military or political support to Bangladesh, however, could irritate New Delhi, in our view, and would be detrimental to US relations with India, a far more strategic South Asian country to overall US interests."
And since you've added
Backing means - aiding in planning and executing the change - designing a plan, supplying with intelligence, helping them organize, running propaganda in favor of the revolution, etc.
Well, if there's evidence of that ... there's evidence of backing, I'm not sure what one might add on this angle.