1. Do I actually need it? For example, I like the gnome ArcMenu extension but I don't really need it, so no to that one.
2. Read the reviews and/or ask in the relevant community, or a Privacy community like this one.
3. If the code's up to date in a repo see where (if anywhere) its phoning home to.
4. If its not but I still really need it, install it, then run Wireshark and see what its up to, if anything.

1. Check for a libre software license text file to ensure we control the software.

How do you judge which extension to install?

• I install as few extensions as possible, like Leraje mentioned already: I really consider if I need the extension or not. Because every single one of them is a potential security or failure risk. One extension may be cool; but if I don't have some real need for it, I won't be installing it. I will also consider native app solutions (I will use yt-dlp in a Terminal instead of using some web extension to easily download vids)
• When I'm interested in one extension, I consider if Firefox is recommending it or not. If not I may decided to not use it. May as it really depends how bad I need it and want to try it.
• I check the options of the extensions I'm already using

1. to disable whatever it is I don't want
2. to enable extra features that may saves me the need to install more extensions. Because, once again, the fewer extensions I have to install, the better I am.

uBO (wikipedia) is an amazing example of that. (edit: I should probably say that I use it on Firefox which supports the extension without limitations, unlike Chrome-based browsers.)

Most people know it as one of the best, if not the best ad-blocker there is. Which it is. But it's much more than that and it can also be used to get rid of cookie banners, url tracking, social media buttons removing (and their tracking), better privacy, I'm sure I'm forgetting some stuff. Heck, it can be used to easily block whatever content I may not want to see on any website. Say, I don't want to see Shorts or News crap displayed on my YT homepage? That's just two clicks away.

So, thx to uBO, I don't need install a shit ton of other extensions I would otherwise be using to get the cleaner and less intrusive web experience I wish. And it only required me to do some reading and tweakings in its settings

Almost all extensions will weaken your security posture. In fact off the top of my head there are basically only two kinds of extensions that could improve it:

• ad blockers
• (maybe!) password manager integrations

Anything else is questionable at best. Maybe you could create browser profiles where you install extensions somewhat more liberally, with decreased expectation of safety.

The site alternativeto.net can help learn more about a piece of software and the alternatives. I have not tried but can you download an extension and run it through VirusTotal? I use that for software all the time.

Like others said, less is more. Also use uBlock Origin to the fullest. It does most of what you need usually. Though it is a pain, I have also started using Noscript again too.