The second diagram places stb incorrectly, because the loop is split into two parallel paths in this point. The first gives a useful loop gain result.
Feedback systems can be designed with multiple cascaded feedback loops. In some cases, it's not possible to identify an overall loop with an insertion point for a loop gain probe. But for the shown system, it's possible I think. There are old Edaboard contributions by user LvW discussing multi-loop feedback systems.
The term "frequency stability" applies to oscillators rather than loop gain analysis.