What's the best code loop-structure to handle multiple tasks without interruption?

[Art]

There are a bunch of PBP commands which cause delay which you can’t use, Pause being a good example,
or at least not with a high value behind it
and some commands that need to be used a particular way which is always contrary to the manual,
in a manner that only deals with bytes at a time. Any serial command is a good example of that.

For the LED display I don’t think any of these enter into it.
Assuming just a loop, your program would be something like:

Set up an initial graphic frame
cycle:
Draw the frame to the LED display
Delay to display the frame to the User
Read input from buttons/interface
Process the next frame based on input and/or the program
goto cycle

As the program progresses it may be the last step increases time to execute,
and the deliberate delay can be shortened or eliminated.
For an LED display it may or may not be helpful to use a timer for the framerate,
but that doesn’t really relate to your question.