My left mouse button is starting to wear out, and as a consequence sometimes a single click gets interpreted as two clicks. Is there a way to force it to timeout for a fraction of a second (I'd have to experiment to find a good value, of course) before it recognizes another click, or some other way in software to work around this issue?

Obviously I can always buy a new mouse, but for environmental sustainability and financial frugality reasons, if I can work around this hardware problem in software to put off when I have to replace it that'd be great.

That sort of thing is often settable in your window manager or compositor of choice. Check its config file.

Have you given the interior of your mouse a good cleaning? It can collect all sorts of dust and crap on wheels and switches. For me, it usually shows up as erratic movement and a mouse wheel that doesn't give smooth movement. (It's an old non-optical mouse - i.e., the tracking is a ball in contact with X- and Y-axis rods that turn optical encoders inside the body, and the mouse wheel is also linked to an optical encoder.)

That doesn't mean that switches don't die, but cleaning is a low-cost effort.