Solution 1:

You can't fiddle with /usr/bin: it's (SIP) restricted. To validate this understanding, just execute

ls -laO /usr/bin

So "resetting" this path as you seek to do is a non-starter.

/usr/bin is full of binaries compiled by Apple themselves. For instance, if you execute /usr/bin/git --version you'll see the git that lives here is an Apple thingy; nothing to do with Homebrew.

I suspect that the programs were already installed by Apple in /usr/bin BEFORE you began installing stuff with Homebrew.