Update, 2024-10-02: This actually does not fix the issue. I've yet to find a permanent solution.

For some reason, with a recent update to the wl-clipboard package or Neovim or both, I started seeing transient wl-clipboard windows, with a corresponding system notification, every time I'd do something that would write to a copy register in Neovim.

It was really annoying.

The fix turned out to be pretty easy in the end. Previously, I'd used this:

set clipboard+=unnamedplus

Switching it over to the following fixed the issue entirely:

set clipboard=unnamed,unnamedplus