Can't switch from voicemail to incoming call without losing messages.

If your incoming calls are going to messages and the volume is lower than usual, it could be due to a problem with the phone settings. Try checking the volume settings on the phone, and make sure the volume is not turned down too low. Additionally, you may need to check the settings for your phone's voicemail, and make sure that your voicemail is not set to kick in after a certain amount of time. If these settings don't help, then you may need to contact your phone's manufacturer for further assistance.

When your iPhone is locked (the screen is off), Do Not Disturb silences all incoming calls, text message notifications, and alerts on your iPhone. Unlike silent mode, Do Not Disturb sends incoming calls straight to voicemail.
https://www.payetteforward.com/why-does-my-iphone-go-straight-to-voicemail-heres-the-fix/

You have unheard messages on the voicemail system provided by your telephone company. This system records messages when someone calls while you're already on the phone. Please contact your telephone company for instructions on accessing their voicemail system.

As for incoming calls, are they possibly going to the aforementioned voicemail system?"

you can contact the service provider...

Your inbox should show messages received. Make sure you have chosen to save your incoming messages

check in settings/phone to see if you have maybe turned on call forwarding and it is being forwarded automatic to your voicemail box number

I don't want to call my voicemail and you can't make me!

We shut the phone system off for about one minute and it reset the system without losing any of the messages.

ask your service provider to erase your voicemail on the phone then add it back again and clearing all msgs

Have you tried going to messages, voicemail, and then pressing "clear" or "clear counter"? i don't know what phone you have so i'm not sure if you have that option...