I have had the exact same experience. I do a little practice every day, but when it come to live action, I have a much harder time. I did see one video where the pro said, "Actual counting of combos is easier on the turn and easiest on the river, where Villain's bluffs are more recognizable and Villain's value hands more obvious and both fewer in number. On the flop, off table practice just gives us mostly a general sense of how Villain's range connects with the board and what we need to be on the lookout for." This perspective accords with how I hear most pros talk about board textures when they are live tabling. For the most part, a pro will say something like, "he's got all the aces, king jack, queen jack, etc, and the Broadway tens in his range as well as medium pairs." Until the hand gets to the river, and then sometimes will get more precise. "He's only got nine combos of ace x which beat me." Or :"He could be bluffing any ace x here, which comes to 24 combos, given Villain didn't 4bet." I think that at this stage and the stakes I play just working on it and trying to implement as much as I can gives me an edge over pool.

There might be some heuristics to keep in mind of this:
Preflop there is 6 combos of each pair, 12 offsuit combos and 4 suited combos of every unpaired hand.
So if we have a narrow range (esp. in 3 or 4bet pots) where we assume that villain will mostly call with pairs and suited combos the thinking process can be simplified:
Imagine having AA as the preflop 3better oop and face a QJ6r board.
We face 9 sets (3x3) and only 2 combos of 2 pairs usually (it would be 3 if QJ wear the same suit), which is only 11(12) total combos of better hands and maybe something like 8 combos of straight draws (KTs/9Ts). So this will be only a pretty small part of villains range that could give us trouble (so we have an easy vbet).
This might get more complex on a 89T-board, but if we can discount most offsuit-combos, this process gets a lot easier (which will often be the case in bigger pots). Blockers might help here as well. So if we had like AQ on QJ6, there is only one set of queens left.
Imo to have a quick overview of the ratio from strong hands to draws in big pots should be kind of most important to have quick in mind. Counting combos with huge ranges in small pots (like BB flat vs BU open) should be less important (as it is usually hard on the fly anyways).
This article would be getting more into deep and gives some more heuristics:

https://www.splitsuit.com/poker-combos-blockers