(1) Programmatic access to the clipboard is something that I expect to get more and more fragile over time. There's already some not-completely-reliable browser logic that stops the clipboard from being interacted with in non-user-initiated contexts. So, rather than implement something that I expect will pick up more and more cross-browser weirdness as time goes on, I think it's better to solve basically the same problem (how finicky it is to copy-paste [code], especially on mobile), but with something that's likely to behave more reliably across more browsers.
(2) The previous patch added the button whether JavaScript was enabled or not. This patch only adds the button when JavaScript is available. Not a big deal, but, it is kind of goofy for the button to be there if it's not going to do anything when you click on it. Better to just not even show it in those situations.
Compared to the version that people helped me test, the only user-facing change I've made is to tweak the opacity (so that it's distinct from the text it's adjacent to, and so that it's a little softer/quieter in appearance):
(That's an image, above. You tried to use that select link/button, didn't you?)