Is there a way to speed up the delay when pressing the home button?
An important navigation mechanism in Android is called a long press. You perform a long press by pressing and holding down a physical key or touch (capacitive) button. If the long press is successful, the phone will provide some physical feedback such as vibration, and the long press action will take place.

You can use a long press to open menus that are specific to the active item - think of it like opening a context menu on a PC. For example, performing a long press on a song in the Music player application in Android 2.2 will open a menu that allows you to add or remove it from a playlist. To perform a long press that opens a context menu, press and hold the select key or the trackball.

Yes you can increase/ decrease  the time duration of the home button under the settings>Accessibility scroll down to Mobility.

Select your desired time gap from the three  -Long/short/medium