>
> Since some recent emacs update (version below):
>
> a) I can no longer generate ≤ and ≥ in Emacs
>
> All combinations (Compose >=, Compose >_, Compose _>) end the same:
> - after entering Compose > there is floating window hinting ≥
> - once I type =, puff, no character in the buffer, nothing.
>

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.

What's that "floating window" you mention?

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