Your
PAGER=less
sets the _shell variable_ `PAGER` to the value `less`. For `man` (or anything other than the current shell) to see this, you will have to additionally make `PAGER` an _environment variable_. You do this with `export`, either through
PAGER=less
export PAGER
or
export PAGER=less
A shell variable is "exported into the environment" with `export`. This is the same in all `sh`-like shells. Exporting a variable in this way is the corollary to the `csh`/`tcsh` `setenv` command.