OK, so PlayStation is an awkward one. It is the same in the Saturn emulator as well.
Firstly I see that you don’t have 224 or 448 resolutions installed. However, the most important part is that these emulators Beetle PSX and Beetle Saturn have hard set vertical heights. these can be changed in the core options. you need to set them so that they match the correct resolution e.g. 16 - 272 this will give you 256p. the difference between them creates the resolution. This will have to match a resolution you have installed.
The annoyance here is that this is not how the original hardware does it! In the original hardware the vertical height changes. However, This is something that the core authors either don’t know about or don’t wish to implement.
I have mentioned many times in the past about Linux. This is because each resolution is installed and removed on the fly. So if you are using the PC just for RA then that could be you better option. This is because currently RA CRTSwitchRes is limited to pre-installed resolution on a Windows environment.
There is a trick to the audio issue. You need to turn audio sync off and manually set the skew to 0.05