Depends on what you mean. If we are talking about whether or not TabFloater itself can be trusted, then I'm 100% confident since I wrote it :) It's fully open source, the companion binaries are built through GitHub Actions, so I have no chance of introducing malicious code. The Chrome extension is also published through GitHub Actions. All this means that you can be sure you're running the same code that you read on GitHub. Publishing the Firefox addon is manual at the moment (they don't offer a great API for automated publishing), but Firefox requires me to submit source code alongside the extension, and they review it.

If you meant an unintentional security issue, then I think we are still good. The only thing the extension communicates to the native application is the title of the current browser tab, which is arguably personal information. However the native application is running on your machine, and you chose to install it. There's no way for remote machines to get your info this way. The only scenario I can see for leaking private info is if someone creates a malware that mimics TabFloater Companion and somehow manages to get it on your machine without you knowing. Then, they will get the titles of the sites you use TabFloater on. There are so many better ways for attackers to get the same information - I think this risk is negligible.

Of course, if you see any other issue that I might have missed, do let me know!

Also have a look at the privacy policy if you haven't already: https://www.tabfloater.io/privacy