It works and was easy to set up. I have everything set to automatically update, so I am not aware of how often that has happened. I haven't noticed anything odd with the phone, and that app has been on it for years now. Google's app does collect data though, so if that is an issue, maybe consider a different one.
Article from PC Mag about the best of these apps for 2024 with pros and cons, on what devices they work best, and if they require an account. If you don't like the link, search for "best authenticator apps for 2024" and the article should be near the top of the list. https://www.pcmag.com/picks/the-best-authenticator-apps
Some that are listed may or may not be recommended by your software.