Hi!
Thank you for all the information regarding the problem.
I’ve looked at the debug data, but strangely it looks perfectly good. I even run one of the queries on my test environment and got results back, I don’t understand the problem yet.
More strangely, when I uncheck the “product” filter on the front-end on the test URL, I get page results if I search “test a” for some reason. I honestly have no idea why is this happening, and I’m not able to recreate it either. I’m suspecting that if the product custom post type is selected, the query fails for some reason(?).
The only thing I can do is to try guessing which part of the query, so I suggest trying these changes:
1. On the General Options -> Sources panel, try turning off the Search all custom fields? option, and make sure no custom fields are selected: https://i.imgur.com/6gYyWQG.png
After that, refresh the front-end and try to search again.
2. If 1. has no effect, then on the same panel turn off the Search in terms? option: https://i.imgur.com/bxBodXw.png
Try the search again, let’s hope that changes anything.
If these change nothing then I might need to see the issue directly. If you can arrange temporary admin and FTP access to a test environment, please contact me via this page and refer to this topic: https://wp-dreams.com/contact/