Delete, or at least hide the messages app in Ventura

Hi community! I wish to work on my mac studio, without ever getting a notification that I've received messages on my phone. I have searched everywhere I can, and have not found a solution. I've tried:

• signing out
• removing the messenger app from the doc
• turned off notifications for messages in System Settings
• 
  

It appears that I cannot simply delete the messages app in ventura, but please correct me if i'm wrong. Even after taking these steps, each time a message goes to my phone, the messages app appears in my dock with a bubble, which I find distracting... and I don't want it! Can you help me?

OS 13.0

M1 chip mac studio