How to determine which brew package provides a given file?

There is not. Nothing in Homebrew maintains a list of files that a package is allowed or expected to install.

While there is not apt-search like tool that allows one to find public homebrew packages that could provide a file, many brew packages are based on a linux or unix counterpart. You can search the Debian package website to find the needed package.

Example for finding package that provides file goocanvas.pc

https://packages.debian.org/search?suite=default&section=all&arch=any&searchon=contents&keywords=goocanvas.pc

Returns libgoocanvas-dev

brew search has no results for libgoocanvas-dev or libgoocanvas but it does have a goocanvas package.

You can define a command ineed as follows that would return a list from debian.org using ineed goocanvas.pc:

ineed() {
echo -en $(echo \
    $(curl -s "https://packages.debian.org/search?suite=default&section=all&arch=any&searchon=contents&keywords=$1") \
       | sed 's%</*tr>%\\n%g') \
    | grep 'class="file"' \
    | sed 's/<[^>]*>//g' \
    | column -t \
    | grep --color -i -w "$1"
}

As stated in this answer you can do ls -l /usr/local//lib/whatever and see where the symlink points to.