Which install or configuration changes into LTS make it lose its LTS essence?

Don't confuse support and stability.

LTS releases offer "stability" in the sense that the software does not change for 5 years, not the sense that it crashes less often. The latter coincidentally does happen to be somewhat true also, but that's due to the large user base discovering and filing bugs.

The best way to keep any release of Ubuntu operating stably (less likely to crash) is to stick to the Ubuntu repositories and Snaps when installing software.

The easy way to make an LTS install unstable (more likely to crash) is to install a lot of non-Ubuntu, PPA, and/or wrong-version software onto it. These are, of course, exactly the same ways that you get dependency problems.

A common problem occurs when folks mistakenly consider an LTS to be a "stable base system" that they can bolt newer software onto. This is precisely the opposite of what an LTS is designed for. If you want newer software, use a newer release of Ubuntu. The Interim (6-month) releases are just as stable for most users as LTS... AND have newer kernel and software.

For a command that details how far from any release (including LTS) that you have drifted, try ubuntu-security-status

$ ubuntu-security-status 
2258 packages installed, of which:
1745 receive package updates with LTS until 4/2025
 499 could receive security updates with ESM Apps until 4/2030
   1 package is from a third party
  13 packages are no longer available for download

Here you can see that I have 14 packages to investigate out of 2258 packages on the system (0.6%). Try it: The output includes instructions on how to get more detail on each category.