Support Arbitrary callbacks

[T4rk1n]

• Allow no output callback, resolve #1549
• Add global set_props, resolve #2803
• Fix side update pattern ids, fix #2111

[ndrezn]

Going to add a few more tests, then we should be almost there!

[emilykl]

Aside from my comments, LGTM. ✨

In general there are a number of places where you've added separate code paths for no_output=True vs. no_output=False and I wonder whether some of them can be condensed down to a single code path... for example if we need to run some processing on the list of outputs, plausibly the same code should work on an empty list of outputs without the need for an if/else (or could be made to work with some small tweaks).