A function is being compiled only on it’s first call, no matter its length in lines of code. There definitely shouldn’t be a minute of waiting time between calling the function and getting to the first line. I’d link this, but as you use a lot of big packages it seems like this would take too much time to reduce.
If you’re able to share code that deterministically shows this behaviour, please do.
As for your other questions - smaller functions in general allow faster execution, since there’s more specialized versions of code available to be called. It may be that the logging notice only showed the problem and in truth the main function itself is slow - in that case, it’d be worthwhile to check @code_warntype for type instability or profile the code. As always, the general performance tips apply.