As outlined in #16816, refactor `ActionMap` to use the new action IDs
added in #16904
## Validation steps performed
- [x] Legacy style commands are parsed correctly (and rewritten to the
new format)
- [x] Actions are still layered correctly and their IDs can be used to
'overwrite' actions in earlier layers
- [x] Keybindings that refer to an ID defined in another layer work
correctly
- [x] User-defined actions without an ID have one generated for them
(and their settings file is edited with it)
- [x] Schema updated
Refs #16816Closes#17133