(summary reply)

>It's unlikely that this is an Emacs bug, Emacs does not "see"
> anything until the compose sequence is finished, it only sees
> the final character.

As I said, I tried in gedit, vscode, firefox, terminator, … –
everywhere this compose clause works. Only emacs fails. And only on
those two sequences.  Considering it fails whichever compose method I
use, I suppose it may have problem with the final char. But note that
copy&paste of the same char works.


> What's that "floating window" you mention?

Attached as floating-window.png (this is what I see after Compose >)


> What does Emacs tell you when you type "C-h k Compose _ >"?

Nothing. It still waits displaying prompt „Describe the following key…"
Same for Compose >= etc.
But when I enter  Compose -> (which work) it displays info about
self-insert-command


> And also what does "C-h l" show _after_ you type those?

…
 <return>                ;; newline
 C-h l                    ;; view-lossage

(I typed this sequence after pressing return)


> Place the breakpoint in handle_one_xevent…

Unfortunately I don't compile emacs myself and don't really have
experience debugging on such level.