In my professional experience, I've found few opportunities to perform literal "by hand" verification.
Unless you're dealing with simple structures (or structures which can be simplified as such), it gets quite complicated and if you perform any mistakes you won't know if it's because of the model or your "by hand" calculation. And I personally have a hard time identifying (non-obvious) mistakes in my own calculations when I'm not even sure they're there.
That being said, the hard part of "by hand" verification of non-trivial structures is the actual structural analysis. Thankfully, the world has many different computer programs that do this exceedingly well.
So I check my work in one structural analysis program by creating another model in another program. This other model, however, is usually much simpler: hell, my tool of choice was Ftool, which only does 2D frame analysis. So if I was trying to double-check a 3D program, I'd have to recreate the model in Ftool using slices, manually calculating the applied loads (usually using simple distribution areas), considering the support conditions (it's much easier to be explicit and intentional about your supports and hinges in 2D than 3D), etc. It's important not to get too detailed in this model: don't try to model a complex support condition using master-slave relations or whatever; make the best simplification you can: fully hinged or fully fixed (or if absolutely necessary, do both and get an average of the results).
And then I let Ftool do its job and give me the internal forces, which I can then compare to the 3D model.
If they're close enough, great. It's much harder to get the boundary conditions wrong in a 2D model (where you explicitly define what they are at a single point, while the 3D model may require you to apply conditions to multiple points to represent the same effect, giving you room for error), so if they're close but actually wrong, it's because you explicitly messed up (i.e. in both models you forgot that that one beam there is actually hinged to the column, not fixed... a mistake you likely would've made even if doing the verification fully by hand). Getting someone else to take a look at your 2D model should further reduce the odds of that happening. And the odds of you having made different mistakes in each model that cancel out to give similar wrong results are infinitesimal.
If they're different, it's far easier to double-check that you didn't mess up your 2D model, and then compare the results to see what's similar and what's different, helping you identify your mistake (while doing it by hand risks a screw up in one element of the stiffness matrix leading you to get everything wrong).
This offers an efficient verification which is quite close to "by hand" -- you are still the one defining the structure's loads, supports and dimensions, in a format (2D) where it's much harder to accidentally mess up the model -- while still being efficient and honestly less error-prone than literally doing it by hand.