If you’re using Google Workspace, Google will give you the appropriate DMARC, DKIM and SPF records to add to your DNS. The NS themselves should resolve the records and provide the recipient server with the values you’ve entered, thereby ensuring delivery.
Does the free DNS on NameCheap no longer allow certain types of records? Aren’t those mail specific DNS records all just TXT/CNAME records now (no more weird legacy SPF record type), which are fairly basic and typical?