You said it is a new phone. Have you by any chance accidentally tapped on “[try/use/activate] enhanced security” when initially setting up the Pixel device?
If “yes,” you cannot access your Google account (or parts thereof, such as Gmail) without having the corresponding account attached and activated on your device. The setup MUST be completed through Chrome for some reason.
You can check in your account if you have enhanced security active. Alternatively, you can try installing an app from an APK/AAB file or from F-Droid. If installation is refused due to enhance security (not due to untrusted source! I literally mean due to enhanced security), the enhanced security is active on your account. You can only install “safe” apps from Play Store (even from there some apps will be blocked from installing).
You can deactivate enhanced security in your account. It will take roughly 24 hours to synchronise through all Google services.