You can find the automated QGIS unit tests in https://github.com/qgis/QGIS/tree/master/tests, for example for vector layers: https://github.com/qgis/QGIS/blob/master/tests/src/core/testqgsvectorlayer.cpp. (There is currently no list of what features are covered by automatic tests.)
These tests are executed every time a developer commits new code to the repository. Helping to extend this set of tests is very important to ensure that nothing is broken by accident.
If your job is to ensure that your custom workflows continue to work after an upgrade, it would seem recommendable to build a test suite that automates testing of these workflows as much as possible.
It is worth noting, that it is recommended to test the development version already during feature freeze instead of waiting for the release - when it is basically too late to avoid shipping a broken version.
As mentioned in the question, it is recommended to use LTR versions in commercial and teaching environments. LTR versions do not receive any new features, only bug fixes. So it is still important to install LTR updates!
Any sufficiently complex software has bugs!