I was able to resolve it by creating a symlink that was missing
sudo ln -s /Users/dacodev/.local/share/containers/podman/machine/podman.sock /var/run/docker.sock
It's not listed as a troubleshooting step but the PodMan docs mention to look for it: https://podman-desktop.io/docs/migrating-from-docker/customizing-docker-compatibility
I'm running PodMan 1.22 and it was not fixed by the previously mentioned PRs but is more likely just due to issues with my machine after a few years of use, installs, uninstalls, etc.
Edit: Another thing I just found is that I had followed the official uninstall method of executing the Docker Desktop uninstaller, but I had originally installed it through Brew. So when running brew remove --zap docker-desktop there were a lot more random dependencies, files, and links that needed to be removed.
brew remove --zap docker-desktop ==> Removing launchctl service com.docker.helper Password: ==> Removing launchctl service com.docker.socket ==> Removing launchctl service com.docker.vmnetd ==> Removing files: /Library/PrivilegedHelperTools/com.docker.socket /Library/PrivilegedHelperTools/com.docker.vmnetd ==> Removing directories if empty: ==> Backing App 'Docker.app' up to '/opt/homebrew/Caskroom/docker-desktop/4.47.0,206054/Docker.app' ==> Removing App '/Applications/Docker.app' ==> Unlinking Bash Completion '/opt/homebrew/etc/bash_completion.d/docker-compose' ==> Unlinking Bash Completion '/opt/homebrew/etc/bash_completion.d/docker' ==> Unlinking Fish Completion '/opt/homebrew/share/fish/vendor_completions.d/docker-compose.fish' ==> Unlinking Fish Completion '/opt/homebrew/share/fish/vendor_completions.d/docker.fish' ==> Unlinking Zsh Completion '/opt/homebrew/share/zsh/site-functions/_docker-compose' ==> Unlinking Zsh Completion '/opt/homebrew/share/zsh/site-functions/_docker' ==> Unlinking Binary '/usr/local/cli-plugins/docker-compose' ==> Unlinking Binary '/usr/local/bin/hub-tool' ==> Unlinking Binary '/usr/local/bin/kubectl.docker' ==> Unlinking Binary '/usr/local/bin/docker' ==> Unlinking Binary '/usr/local/bin/docker-credential-desktop' ==> Unlinking Binary '/usr/local/bin/docker-credential-ecr-login' ==> Unlinking Binary '/usr/local/bin/docker-credential-osxkeychain' ==> Dispatching zap stanza ==> Trashing files: /usr/local/bin/docker-compose.backup /usr/local/bin/docker.backup ~/.docker ~/Library/Application Scripts/com.docker.helper ~/Library/Application Scripts/group.com.docker ~/Library/Application Support/com.apple.sharedfilelist/com.apple.LSSharedFileList.ApplicationRecentDocuments/com.docker.helper.sfl* ~/Library/Application Support/com.apple.sharedfilelist/com.apple.LSSharedFileList.ApplicationRecentDocuments/com.electron.dockerdesktop.sfl* ~/Library/Application Support/com.bugsnag.Bugsnag/com.docker.docker ~/Library/Application Support/Docker Desktop ~/Library/Caches/com.docker.docker ~/Library/Caches/com.plausiblelabs.crashreporter.data/com.docker.docker ~/Library/Caches/KSCrashReports/Docker ~/Library/Containers/com.docker.docker ~/Library/Containers/com.docker.helper ~/Library/Group Containers/group.com.docker ~/Library/HTTPStorages/com.docker.docker ~/Library/HTTPStorages/com.docker.docker.binarycookies ~/Library/Logs/Docker Desktop ~/Library/Preferences/com.docker.docker.plist ~/Library/Preferences/com.electron.docker-frontend.plist ~/Library/Preferences/com.electron.dockerdesktop.plist ~/Library/Saved Application State/com.electron.docker-frontend.savedState ~/Library/Saved Application State/com.electron.dockerdesktop.savedState ==> Removing directories if empty: ~/Library/Caches/com.plausiblelabs.crashreporter.data ~/Library/Caches/com.plausiblelabs.crashreporter.data/com.panic.Transmit ~/Library/Caches/com.plausiblelabs.crashreporter.data/com.panic.Transmit/queued_reports ~/Library/Caches/com.plausiblelabs.crashreporter.data/com.larian.bg3 ~/Library/Caches/com.plausiblelabs.crashreporter.data/com.larian.bg3/queued_reports ==> Removing all staged versions of Cask 'docker-desktop'
