If I read homebrew's install.sh correctly, it changes ownership of a few directories under /usr/local, not /usr/local itself (on x86, on ARM it follows a different path). This matches how my current Mac, which has brew, is currently setup as well.

    # Required installation paths. To install elsewhere (which is unsupported)
    # you can untar https://github.com/Homebrew/brew/tarball/master
    # anywhere you like.
    ...
        # On Intel macOS, this script installs to /usr/local only
        HOMEBREW_PREFIX="/usr/local"
    ...
    directories=(bin etc include lib sbin share opt var
                 Frameworks
                 etc/bash_completion.d lib/pkgconfig
                 share/aclocal share/doc share/info share/locale share/man
                 share/man/man1 share/man/man2 share/man/man3 share/man/man4
                 share/man/man5 share/man/man6 share/man/man7 share/man/man8
                 var/log var/homebrew var/homebrew/linked
                 bin/brew)
    group_chmods=()
    for dir in "${directories[@]}"; do
      if exists_but_not_writable "${HOMEBREW_PREFIX}/${dir}"; then
        group_chmods+=("${HOMEBREW_PREFIX}/${dir}")
      fi
    done
    ... and further on, after some checks, group_chmods turns into chowns ...
    if [[ "${#chowns[@]}" -gt 0 ]]; then
      ohai "The following existing directories will have their owner set to ${tty_underline}${USER}${tty_reset}:"
      printf "%s\n" "${chowns[@]}"
    fi

Haven't used Homebrew in quite a time, so I'm not sure.

'ls -l /usr' reveals that /usr/local is root:wheel just like all other folders under /usr. How exactly is homebrew changing ownership?

Anyway, this requirement is well documented and not new:

https://github.com/Homebrew/brew/issues?q=is%3Aissue+%2Fusr%...

http://github.com/Homebrew/brew/blob/master/docs/Installatio...

Homebrew asks users (on Intel macs) to change the ownership of /usr/local to their local user. And it refuses to run under sudo.

Nope - intel Mac on Big Sur:

drogers@SJCMACJDYMD6M ~ % ls -l /usr

[snip]

drwxr-xr-x 15 root wheel 480 Dec 14 20:10 local

[end snip]

And for the record, neither of your links support your claim.

https://apple.stackexchange.com/questions/1393/are-my-permis...

https://superuser.com/questions/1264673/chown-usr-local-oper...

No, I'm on an Intel chip, not M1.

>Homebrew asks users (on Intel macs) to change the ownership of /usr/local to their local user. And it refuses to run under sudo.

Again, no, not on my machine it doesn't. /usr/local is root:wheel. This is a newish (to me) machine that I gave first birthday to beginning of December 2020. The first thing I did was installed brew and started installing the things that makes my computer useful to me. No permissions were asked to be changed.

Dunno if it needs this now anymore -- i think they moved to /usr/local/Homebrew some time ago -- but this was a big deal for a few years