Just for time tracking? That seems overkill to me, in terms of having to manage the app downloads, installs, and updates across multiple machines. And I'd worry about security concerns. The Chrome extension is tied to your user profile and auto-synced across browser instances when you log in, and is just a tiny bit of JS that's sandboxed and subject to Chrome's robust permission model. I'd choose that over a desktop app any day for something as simple as a time tracker. This is the one I use, and I think it's not even an official Harvest app but a third-party thing that hooks into their API: https://chromewebstore.google.com/detail/harvest-time-tracke... (edit: My bad, it DOES seem like an official app)

On the other hand, if you were thinking of building the full web app into a native experience, then yeah, a desktop app would be better than an extension. But I still probably wouldn't use it over the regular website, especially if it were just an Electron/Webview wrapper anyway. In my experience the desktop apps/PWAs tend to be clunky and limit the UI in some significant way (such as not being able to easily right-click, or see the URL bar, or use uBlock, or easily silence notifications or prevent on-launch updates, etc).

My work currently uses Basecamp and I tried their desktop app once or twice, but it was so bad I went back to the website.