The problem with terminfo is that not every tool relies on it. I've seen many examples (hello, exa), when the codes are hard-coded to operate with xterm-256. So, I decided to pretend to be an xterm.
The problem I see is that you seem to have the terminal doing things like fuzzy matching input against PATH executables. But that's the shell's domain. The terminal should just expose commands for adding text items to a drop down under the cursor, and the shell should send the matches to the terminal. And capabilities like this should be clearly defined in a terminfo page (which you should definitely have, even if for non-custom capabilities it uses the same definitions as xterm), so that well-written apps can send this information if and only if those capabilities are defined.
Of course this is a huge challenge, because if you do it this way your terminal doesn't do anything new until someone writes a program to run in it using its extended capabilities. So this creates a chicken and egg problem. But you can't come up with nearly as many interesting things for your terminal to do with cursor dropdowns as everyone in the world can if you're just exposing that in the same way the character grid is exposed.
Perhaps unexpectedly, Black Screen is both a terminal emulator and a shell. I tried hard to avoid going with writing a shell, but the existing ones simply don't fit. It's even hard to know when a child execution has finished. And I want smart autocompletion, so I have to at least extend a shell.
Traditionally these two are separated, and it must be a good design, but my current goal is to prove the concept. Perhaps, later I'll extract the shell.
Just like the web itself, any new teminal client needs to be backwards compatible with the capabilities of prior terminal clients, because programs that run in the terminal expect it. And if your terminal can't run the programs everyone runs in their terminals, no one will adopt your terminal. But many of these projects seem to have no intention of maintaining that backward compatibility. Some, like TermKit, fully conflate the terminal and the shell and even many UNIX utilities.
You can't hope to supplant ANSI compatible terminals when you let them have the enormous advantage of running all the software anyone wants to run in a terminal that already exists. It would be like saying you have a new, better web browser that can't open any existing web pages.
No idea if this particular project has learned from past examples and is backwards compatible or not. (EDIT: It doesn't have a terminfo page, so probably not.)