Weird/broken scrollback handling when using tmux at remote ssh host (alternate buffer?)

[bago]

Windows Terminal version

1.22.3232.0

Windows build number

10.0.19045.5247

Other Software

OpenSSH_for_Windows_9.5p1, LibreSSL 3.8.2 (also tested OpenSSH_for_Windows_9.8p1 Win32-OpenSSH-GitHub, LibreSSL 3.9.2)
tmux 3.2 on the remote host using this tmux.conf:

set-option -ga terminal-overrides ',xterm*:Tc:smcup@:rmcup@'

Steps to reproduce

Open an ssh session to a remote linux host.

test normal scrolling behaviour

for i in $(seq 1 1000); do echo $i; done;

look at the scrollbar and/or try to look at the scroll CTRL+SHIFT+PgUp or the mouse wheel, everything works as expected.

now run the same inside tmux:

tmux
for i in $(seq 1 1000); do echo $i; done;

I can still try to scroll back but I don't find the real output of my loop command.

I tested a lot of terminal emulators for windows and none of them works but Putty: Putty correctly let me scroll back when I'm in tmux the same way I do when I'm outside tmux, and that's why I guessed the issue is in the terminal and not in tmux/tmux configuration (but I know things may be more complex).

Expected Behavior

Being able to scroll previous output pages also when I'm using tmux

Actual Behavior

Previous output pages generated inside tmux are lost (I can see them with tmux internal scrollback but not in a way integrated with Windows Terminal scrolling).