With no labels I could not be sure what comes from where. It's a bit daunting to follow all the text in these posts and then try to connect what what is what in the diagram.
Looks like you have 2 sources of 5V power?
One that powers the ATXRaspi (from wall?) and one that powers everything else? Are they common ground?
The switches you have are probably SPST (single pole single throw). The latching just ... latches in the closed position. They happen to have a COM and NO (normally open) + NC (normally closed) connections, you want them wired from COM to NO, such that when the switches are PRESSED (either latching or not) the connection is closed.
No ground is needed, unless the COM is grounded and the NO is pulled up. I recommend never to copy paste what you see in amazon comments and then turn it on to see if it works.
No offense but in electrical/electronics work it's required to understand what you're doing or things can blow up (low power electronics) or you can get killed (with mains), it's not a joke.
I'm glad you got the ATXRaspi working, means I'm doing a decent job with the guide