The name servers themselves is not part of the equation. The commonality in all those linked are sending emails from Namecheap’s shared hosted email/website, not name servers. Sending email from shared hosted email/website is asking for trouble, doesn’t matter who you’re hosting with, because those IP range are always abused, especially with the larger providers, simply due to a larger exposure. The detection mechanism here is really simple and observable via raw mail headers by checking the Received: line. Filtering emails from this information here is a typical part of the anti-spam model. A typical implementation would be via DNSBL providers such as Spamhaus, Sorbs and alike. The solution is always to use trusted transaction email services to deliver email from the website instead.
That, however, is a very different problem than the dedicated email services like Google Workspace Gmail, because you’d not be sending from your web server’s IP address, but rather via Google’s dedicated range. As such, the Recevied: line is much less likely to yield a match in DNSBLs. Validation for these are then done via the SPF/DKIM/DMARC records on your domain, checking if your configuration permits delivery from server at the Recevied: line (look for Received-SPF) and whether or not you have the appropriate signing (look for Authentication-Results: and bits about the various stages of DKIM and DMARC).