The issue you are experiencing is most likely related to a feature called "ear detection". This feature automatically turns the audio off when you place the iPhone to your ear, assuming you are trying to take a call. To resolve the issue, you can disable the ear detection feature. To do this, go to Settings > Accessibility > Touch > and toggle off the 'Ear Detection' option.

If it started after updating to iOS 16, it may be related to that. I don’t know how to fix it if the problem is due to the iOS/ hardware.

I would troubleshoot to see if it is a software issue.

There are a couple of things that might be happening. What you described happened to me years ago on my iPhone 4, but that was failure of the phone’s ear speakers. I had to use speakerphone to hear voicemail because those speakers still worked. There are a whole lot of settings to try before concluding it’s a hardware issue.

Since automatic ear detection was not the problem, I’d turn that back on.

Make sure your phone is backed up.

To troubleshoot in case it’s not a hardware problem, there are a few things you can try (list compiled of what I’ve tried and what I could find):

• Do not disturb- make sure it’s off
• Make sure the volume for calls is actually up. Try increasing the volume while actually trying to listen to a voicemail or make a call. When you're on the phone or listening to songs, movies, or other media on iPhone, you can use the buttons on the side of your device to adjust the audio volume. Otherwise, the buttons control the volume for the ringer, alerts, and other sound effects. You can also use Siri to turn the volume up or down. Keep in mind volume for calls only works while you are making/listening to a call, as those settings are independent.
• Check Settings > Accessibility > Touch > Call Audio Routing and make sure that your call audio routing is on automatic.
• Try restarting your phone
• Update your phone to the latest software.
• If there’s no sound coming out of the iPhone’s ear speaker, ensure it’s set as the audio destination and not your AirPods or another Bluetooth headset you might be using regularly. To do that, tap the Audio icon while on a phone call and select iPhone. Alternatively, turn off any Bluetooth devices or disable the Bluetooth radio on your iPhone (open the Control Center and tap the Bluetooth icon).
• Do you use wired earphones or headphones with your iPhone? It’s common to have the audio stuck in Headphone Mode even after removing your headset. The Volume slider in the Control Center will display a Headphone symbol when that happens. Although it’s possible to switch to the ear speaker manually during a phone call, that can be a recurrent problem unless you get your iPhone out of Headphone Mode. To do that: Plug your headphones into your iPhone and out again. Clean out the headphone jack or Lightning connector very carefully. Force-restart your iPhone.
• To check the speakers, go to Settings > Sounds and drag the Ringer And Alerts slider to turn the volume up. You should hear the ring tone clearly. To check the microphone, use the iPhone or iPad's standard Voice Memos app. Open the Voice Memos app or ask Siri to open it and speak into the microphone.
• If your phone speaker volume remains low even after turning the volume to the highest, your phone speaker may be clogged. Try cleaning your speakers, then try your calls again to see if the problem is fixed. Update your iPhone. Something as simple as an outdated operating system or speaker driver could be why you're having trouble hearing callers on your iPhone.
• Go to Settings > Sounds (or Settings > Sounds & Haptics), and drag the Ringer and Alerts slider back and forth a few times. This can help reset the sound toggles.
• Phone Noise Cancellation is supposed to cancel background noise, but if it’s not working correctly try turning it off. Open Settings > Accessibility > Audio/Visual > Turn off Phone Noise Cancellation.
• Some software problems can be difficult to track down. Try resetting all the settings on your iPhone. This will reset everything in the iPhone Settings app back to factory defaults. You’ll have to set up your wallpaper again, reenter your Wi-Fi passwords, reconnect your Bluetooth devices, and more. Open Settings and tap General -> Transfer Or Reset iPhone -> Reset -> Reset All Settings.
• If you still don't hear any sound, or if your speaker button on the Ringer and Alerts slider is dimmed, your speaker might need service.