FYI I'm not trying to diminish your project, and I'm glad you've made something which scratches your exact itch. I'm also hopeful others will like it.
I can't answer for others, but personally I don't like the zsh-like way to "show the possible completions in dark grey after the cursor" because it disrupts my thoughts.
It's pull vs push: whether on the commandline or using an AI, I want the results only when I feel I need them - not before.
If they are pushed into me (like the mailbox count, or other irrelevant parameters), they are distracting and interrupting my thoughts.
I love optimization and saving a few clicks, but here the potential for distraction during an activity that requires intense concetration would be much worse.
I can somewhat accept it showing an option if 1) it's the only one, 2) it's not rapidly changing with my typing. I know what I want to type before I type it or know I'm unsure what to type. In the former, a completion is only useful if it correctly matches what I wanted to type.
In the latter, what I'm typing is effectively a search query, and then completion on typing might not be so bad, but that's the exception, not the norm.
It's annoying when a pushed prediction is wrong, but when it's right it's like coding at the speed of thought. It's almost uncanny, but it gets me into flow state really fast. And part of that is being able to accept suggestions with minimal friction.
Perhaps that would be advantageous here too?
I don't use Emacs any more, but I'll likely take pretty much the same approach for my own editor.