Custom domain with Namecheap using Namecheap basic DNS

This is not correct. You can use external DNS configuration.

This is also not correct. You would add these records to Netlify DNS. Read

Instead of the simple Gmail configuration available in Namecheap, you would need to configure the MX records. Read: Google Workspace MX record values - Google Workspace Admin Help

And it would appear you have successfully configured Netlify DNS after all that.