How to search the whole manual pages on Linux?

From man man:

-K, --global-apropos
      Search for text in all manual  pages.   This  is  a  brute-force
      search,  and is likely to take some time; if you can, you should
      specify a section to reduce the number of pages that need to  be
      searched.   Search terms may be simple strings (the default), or
      regular expressions if the --regex option is used.

This directly opens the manpage (vim, then ex, then gview, ...) for me, so you could add another option, like -w to get an idea of which manpage will be displayed.

$ man -wK viminfo
/usr/share/man/man1/vim.1.gz
/usr/share/man/man1/vim.1.gz
/usr/share/man/man1/gvim.1.gz
/usr/share/man/man1/gvim.1.gz
/usr/share/man/man1/run-one.1.gz
/usr/share/man/man1/gvim.1.gz
/usr/share/man/man1/gvim.1.gz
/usr/share/man/man1/run-one.1.gz
/usr/share/man/man1/run-one.1.gz
...

Use the global apropos option in man.

 -K, --global-apropos
              Search for text in all manual pages.  This is a brute-force search, and is likely to take some time; if you can, you should specify a section to reduce the number  of pages that need to be searched.  Search terms may be simple strings (the default), or regular expressions if the --regex option is used.

So, man -K viminfo will give you the page you need.