sentry-java VS Bugsnag

>As now we've introduced some peers code review, automatic testing on most critical stuff (but since the codebase sucks these aren't really reliable tests)

They may not be "reliable", but these are your safety net, or harness, so you don't fall. I wrote about similar issues, for instance here: https://news.ycombinator.com/item?id=26591067 and, given your promotion, here: https://news.ycombinator.com/item?id=37211796. It contains a few steps starting from "So...".

You can add monitoring, something like Sentry (https://sentry.io) will capture exceptions that were not handled that you have not seen because the stack trace is buried in hundreds of pages of logs or something. It groups them by exception and counts them. It's pretty awesome. (https://docs.sentry.io). It supports around 108 platforms (Java, Python, JavaScript, etc.). This lets you see the exceptions and makes prioritizing easier (which ones are the most frequent, which ones impact the most, etc.).

If you don't have them already, issue templates are really useful and the comment I linked to explains why, but here's an example of an issue template (again, you can configure them for different types of issues so team members select from a dropdown for a bug or a feature):

But, from my understanding, it targeted only software developers that would like to have super-deep insights into the applications and is not intended for monitoring simple apps like websites. Also, I have no idea even if I embed it, whether will it be able to tell me if my resources loaded or the performance didn't go well. For example, I don't see how I can easily embed it into my website: https://docs.sentry.io/ only programming languages are listed here.

Sentry provides informative guides for many platforms. In our server's case, we apply Apollo Server v2 as an Express middleware; therefore, Sentry's Express Guide with request, tracing, and error handlers is a great starting point.

The last step is to extract the openReplaySessionToken from the header and add it to your Sentry scope (ideally using a middleware or decorator) in your backend. The method to do this depends on the programming language of your backend, you can consult the Sentry docs on how to configure scope. The snippet below shows how to configure a Sentry scope if your backend is built with node.js/express

In a lot of cases crash report SDKs are open source?

Sentry: https://github.com/getsentry/sentry-java

It appears so: https://github.com/bugsnag/bugsnag-android/blob/master/LICENSE