When viewing the map, I get the the following message and the map is coming as developer mode with grey background. How do I avoid this?

Google Maps Platform recently made API key mandatory for some regions and scenarios. Please refer How to generate API Key for more details on this and to setup key.

Why can't we see the One Tap sign-in prompt on the embedded map?

We have migrated to FedCM (Federated Credential Management) authentication to enhance user privacy. This issue may be due to the FedCM API requirements. To ensure that the One Tap sign-in works correctly when embedding an iframe, you need to add the allow="identity-credentials-get" attribute to each of your iframe tags. This attribute enables the necessary permissions for the One Tap API to function in cross-origin iframes.

Example:  <iframe src="https://your.map.example" allow="identity-credentials-get" width="100%" height="600px"></iframe>