Turns out that Unity wasn't receiving the correct path. I think this would be true for most applications launched from the Dock, Finder, or Spotlight (but not from the Terminal). (It's not the case for MacVim, but that's unsurprising so I didn't dig into why.)
It had this set for PATH:
My .bashrc, .zsh_profile, etc didn't effect the PATH.
This post explains that on macOS you need to use launchctl to set your PATH for it to be respected by apps launched outside of a shell. Since I have svn from brew, it's in
sudo launchctl config user path /usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin
Once I'd done that, rebooted, closed, and re-opened Unity, then it found my brew-installed svn.