This solution allow to use putty's sessions inside Windows Terminal and not only.

Just execute psh and choose required session.

1. git clone https://github.com/SailorMax/psh.git
2. execute psh.bat. It has to output all putty session names and suggest to choose anyone to connect. In case of session_chooser.ps1 is not executable try: right mouse click on ps1-file / Properties / Unblock
3. add to PATH your clone-directory and directory of the putty (SystemPropertiesAdvanced / Enviroment Variables... / User variables)
4. open Windows Terminal and execute psh (as second argument you can use word to filter sessions list or directly host:port)
   
   

1. remove from memory git's ssh-agent (via task manager), remove user's variables SSH_AGENT_PID and SSH_AUTH_SOCK (via SystemPropertiesAdvanced / Enviroment Variables...), remove from PATH directory of Git's (or similar) ssh (if it exists there)
2. install via Windows "Optional features" OpenSSH client
3. if actual, prepare Git to use system's ssh: git config --global core.sshCommand "'C:\Windows\System32\OpenSSH\ssh.exe'"
4. if require, prepare file similar to config/add_default_key_to_agent.bat or use this one in manual setup ssh-agent ("WinSSH" keep them between restarts).
5. to use new PATH some programs require restart

(!) Warning! Some programs still doesn't support "WinSSH" (DBeaver, for example). For them you can try to use Putty's Peagant as separate process. Or setup variables SSH_AGENT_PID and SSH_AUTH_SOCK for "WinSSH".