Your comments

The built-in Mecanim state machines kinda sets the expected language in Unity.

There is an Entry state and an Exit State always. And the AnyState node quits current active state (allowing an override whatever the state was).

"Currently, the Any State unit exits only directly connected outgoing states.": Can you elaborate what this means? I was having this exact same issue and maybe this would solve it, where triggering a restart of the state machine would leave the last one still hanging on update (and it won't trigger an enter event if it gets back there).

Could go as far as: 1 on the keyboard + Click creates a float, "2"+Click creates a vector2, T+Click triggers, etc.

Also find very useful the idea of the first letter being pressed triggers the search box right away.

Was going to come here to suggest this same idea. It's a good one. Would be nice to see it documented with more visibility.