Glad to hear it's useful for you!
Regarding Chrome, I haven't updated the (sideloaded) extension to Manifest V3 yet, which is why it can't be installed under newer versions of Chrome. I'm not sure if it's possible or not without reducing its featureset, but it's something I'll look into in the future.
In the meantime, if you do still want to use it with Chrome browsers, you can still use it as a userscript (using something like Tampermonkey or ScriptCat), which has most of the functionality of the addon.

Google Images recently updated, and the previous technique to find the original images past 100 (the preloaded amount) doesn't work anymore. I've implemented a fix for the userscript version, but unfortunately getting this to work on the extension version is a bit trickier, and might not land in the next release (it needs to intercept HTTP calls, which is definitely my least favorite approach towards supporting a website).
I've tracked the feature here: https://github.com/qsniyg/maxurl/issues/1533 . Note that once it's implemented, you will need to enable "Rules intercepting HTTP requests" (under the Rules tab). It's disabled by default because it carries a fingerprinting risk.

Sorry, this is a bit of a long response, but I'd like to address to your concerns.

To address the info stealing/malware concern, the script is 100% open source ( https://github.com/qsniyg/maxurl ), and does *not* collect any kind of data about you. As part of being in the "Recommended extensions" program, Mozilla thoroughly audits these addons, and has actually requested a few changes in the past (that were implemented) in order for the script to be even more transparent to its users.

Regarding how it works, this addon finds larger images present *within* a website. Many websites will store an original full-sized image, but instead link to a smaller/scaled down version of the image. This is what the (currently) ~5800 rules do, as each website will often have their own systems to resize images.

It doesn't replace using a reverse image search, but rather complements using one. I personally regularly use both a reverse image search engine (such as Yandex, as you mentioned) alongside this addon, and have found that reverse image search engines often link to scaled down images that this addon finds a larger version of present on the website.

I would recommend enabling the "Enable redirection" (under the Redirection tab) and the "Rules using API calls" (under the Rules) tab. These options are disabled by default for users' privacy as they must perform HTTP requests to find the larger image, but they will help by (respectively): #1 Automatically redirecting images opened in their own tabs to the larger versions stored on the same site (if applicable), and #2 Supporting ~20% more websites, which require website-specific API calls to find the larger version (e.g. Flickr).

If you have any further questions or concerns, please feel free to reach out using any of the communication methods at the bottom of the addon's description (discord/email/github etc.) :)