The current trend in the unified comms is moving to proprietary interfaces. TAPI does not really have decent facilities to deal with the addition of chat and video channels anyway. While some vendors seem to be willing to keep supporting it for some time, most seem to be designing new API's from the ground up (Teams Graph, Cisco WebEx, Alcatel Rainbow,...)
Specifically to your question: no, Teams does not support TAPI and there seems to be no intention to ever do so. None of Microsoft previous UC solutions (Skype for Business, Lync, Office Communication Server) did either.
If you don't want to develop/test straight onto your production Cisco, you may be able to get a VM version of the PBX with a trial/temporary license for software development purposes through a Cisco partner.