Iphone 7, 8 and SE2020 home buttons do not press it, they are pressure sensors. There should however be a "haptic" response that feels like a click but only when the phone is powered up. The loss of that seems to be related to the general loss of sounds and haptics.
You may have a hardware problem.
The next procedure would be to backup then restore your device to factory, and setup the device without restoring a backup, to see if the issue is replicated.
Then restore the backup.
If you need to send the phone in for repair then backing up and restoring to factory would be needed anyway.
Here is a guide for those steps
Backup and restore
(1)How to back up your iPhone, iPad, and iPod touch – Apple Support
Remove SIM PIN if you have set one
(2) Restore your iPhone, iPad, or iPod to factory settings – Apple Support
Set up as new from the Hello Screen without restoring backup. Test if the problem still exists
(3) Restore your iPhone, iPad, or iPod touch from a backup
If that fails arrange a repair
https://support.apple.com/en-gb/iphone/repair/service