Uninstall

In the app, with Homebrew, or by hand. None of them moves a single one of your downloads back.

In the app

General › Other › Uninstall…. It removes the login item, its settings, the history and the log, then quits and opens Finder on the app so you can drag it to the Trash.

With Homebrew

brew uninstall --cask tideline

# or, to take its settings and log with it
brew uninstall --zap --cask tideline

By hand

osascript -e 'quit app "Tideline"'
rm -rf "/Applications/Tideline.app"
rm -rf "$HOME/Library/Application Support/Tideline"
rm -f  "$HOME/Library/Logs/Tideline.log"
defaults delete be.eliostruyf.Tideline

Then, optionally, remove the leftovers macOS keeps:

System Settings › General › Login Items — remove Tideline if it is still listed.
System Settings › Privacy & Security › Files and Folders — remove its Downloads Folder permission.

Your files stay where they are

Uninstalling never moves a file back. Your downloads and every dated folder stay exactly where they are. If you want the folder as it was, use Put Everything Back… before you go — once the app is gone, so is the record of what it filed.