My employer currently pays a lot of money for TeamViewer licenses, just to connect to some internal machines.

I think a more reasonable approach is to understand your threat model and act accordingly. If you need to remotely access a PC and are concerned about TLAs, maybe audit the source code directly. Or like another commenter noted, do direct IP connection between two devices on a Tailscale network.

Teamviewer pissed me off when they stuffed up my payment, reversed the charges without telling me, then sent me a letter saying they were taking me to court.

I found rust desk after that and have sworn never to pay Teamviewer a cent.