In VisualGDB Properties page, When selecting a different Pico SDK Version in the pull-down list, clicking on [Apply] just puts the previously selected SDK back, it doesn’t keep the new selected SDK. I had done this in the past, and it worked; but haven’t tried it for a long while. It’s version 5.6R9(build 4777).
So, it appears that the new selected SDK is used for compile, just the properties page puts the name of the previously selected SDK in the pull-down when trying to change it and using the [APPLY] button.