Thank you for your update.
Setting rules on Gmail Web is indeed a better choice, as I mentioned earlier. Using Webmail's automated rules to handle emails directly is more effective and stable since it runs on the server and does not depend on the application running.
I'm very glad that it worked for you. If you find my response helpful, you can mark it as "Yes." This will provide valuable experience and reference for other members of the community. Thank you very much for your contribution. Have a great day.
Best Regards,
Zachary.W - MSFT | Microsoft Community Support Specialist