You should be able to paste using the (annoying, yes) CUA key Shift-Ins vs. right mouse button.

I think the only way to know for sure you're under putty is to change your putty configuration to set/send a custom environment variable that you can test. I do not recall one that it sets/sends by default beyond TERM which is "xterm" and that's obviously insufficient.

On Mon, Dec 23, 2024 at 1:47 PM Eli Zaretskii <eliz@gnu.org> wrote:
I found one more case where turning on xterm-mouse-mode by default
causes problems: PuTTY.  It loses the ability to paste from the
Windows clipboard by a right mouse click when xterm-mouse-mode is
turned on.

Can we identify PuTTY in some way, so that xterm-mouse-mode could not
be turned on in that case?