Microsoft Teams is not listed on my iphone's privacy microphone setting

df777 The PG responded with a whole set of options for you to try. It's not a known issue and they can't pinpoint with certainty, but hopefully one of these can help you out.

Please also let me know if this helps you resolve it.

Managed device

Do you happen to have your device managed by your company? It might be that they have a policy to block the usage of the microphone.

Reset network settings

Go to Settings > General > Reset > Reset Network settings. Your device might restart automatically, but if it doesn't, please restart manually. You will have to reconnect your network settings when your device reboots. Afterwards, open Teams and it should now prompt you for mic access.
Just to be clear, there is impact doing this reset. Please check out this page to be fully informed: https://www.howtogeek.com/270185/how-to-reset-your-ios-devices-network-settings-and-fix-connection-issues/
Fix comes from Apple support forums: https://discussions.apple.com/thread/251269841

No apps are showing under Privacy -> Microphone

Looking at your screenshot of that page, you have no apps in there. I have multiple, some very high profile: Facebook, Skype, WhatsApp, etc. If you really don't have any of those apps on your device, it's ok, but if you do: there might be a phone failure here.
Even apps that you don't have approved should show up.

As a general test, can you try installing "Skype" consumer app? It should also prompt you and show up in that list.

Teams for Personal

Last option: uninstall Teams app, reinstall. Upon opening the app, sign up for a Teams for Personal account with your personal Microsoft account. This should also trigger the microphone ask again.