If the issue is just in setting up PAMGuard to do what you need, I think the below should help you. If it is a bug or other issue and you've already done this, then maybe you can share what you have for these settings as well.
STEP 1. To batch process multiple files:
- Select "Audio file folder or multiple files" as the Data Source Type in the Sound Aquisition settings window. To access that window (which you have shown in your first screenshot, but just for others who might find this helpful) select Settings > Sound Aquisition and then click on "Data Source Type" to access the dropdown menu
- Then, when you browse for the files, you can either select an entire folder, or select multiple files by holding down ctrl and clicking all the files you want
STEP 2.
You also need to set up an output database and binaries folder to save all your results in one place. It saves them as an SQL database, but the tools that @Chloe pointed to in her answer will allow you to read that database into Matlab.