I believe this is not so much about man
itself but rather about your pager of choice (PAGER
environment variable) combined with the terminal in use.
I’m guessing your pager is probably less
(typical default pager nowadays and fits with the description).
less
has an option -X
that may get you a behavior along the lines of what you’re looking for.
-X or --no-init
Disables sending the termcap initialization and deinitialization
strings to the terminal. This is sometimes desirable if the
deinitialization string does something unnecessary, like clear‐
ing the screen.
Eg PAGER="less -X" man man
could be used for testing it out, and if you find this behavior preferable you might consider setting PAGER
to this value permanently.