If you are not managing your clients' Macs, they either need an admin password for installation or can use QuickSupport.

If you are managing your clients' Macs using an MDM, you can deal with everything using your MDM system, except for Screen Recording consent, which needs to be given by the user and does not require an admin password.

Assuming you have already given permission to TeamViewer for Accessibility and Screen Recording, Full Disk Access can be configured remotely by going to System Preferences during a TeamViewer Remote Control session.Consent can be given by the user in System Preferences > Security & Privacy > Privacy > Full Disk Access. An admin password is required.To my knowledge, Apple currently provides no way to permit screen recording through MDM.

Consent can be given by the user in System Preferences > Security & Privacy > Privacy > Screen Recording.

For Macs in an organization, this can also be permitted by the admin using an MDM system through Privacy Preferences Policy Control (PPPC) payloads.

Consent can be given by the user in System Preferences > Security & Privacy > Privacy > Accessibility.

Full Disk Access to browse/access all files and folders on disk for File Transfer (since macOS 10.15).

Screen Recording to capture screen contents (since macOS 10.15).

Accessibility to control the Mac's mouse/keyboard (since macOS 10.14).

TeamViewer is required to obtain user consent to use these features:

The OS now requires explicit user consent for apps to be able to access certain functionality. In recent years, Apple has tightened privacy and security in macOS. To install TeamViewer on a Mac, an admin password is needed. If you are managing the users' Macs, installation can of course be automated using whatever tools you normally use to deploy packages to their systems. And, as there's also the possibility of using TeamViewer QuickSupport – no installation (or admin password) required. there are two parts to having everything up & running on macOS Catalina (10.15).

To add a few more specific infos on top of what mentioned.

Where does teamviewer install on mac