Windows currently has no built-in option to open File Explorer automatically after pressing Print Screen.
The closest method is to press Windows + Print Screen. The screenshot is saved directly to Pictures > Screenshots. You can pin this folder to Quick access for faster access.
For Snipping Tool, open it, select … > Settings, and enable “Automatically save original screenshots.” Microsoft’s instructions are here: https://support.microsoft.com/en-us/windows/apps/use-snipping-tool-to-capture-screenshots
To make the folder open automatically after every capture, a custom script or third-party screenshot tool would be required. You may also submit this feature request through Feedback Hub by pressing Windows + F.