Recently, I just purchased a domain from AWS by using Route 53. The problem is that I want to point this domain to a wordpress website that lies in Vultr host, but even thought I changed the NS record on Route 53 to Vulture's and test it by using https://www.dnswatch.info/, it still cannot open my website when I enter new domain to browser. I got little knowledge when it comes to DNS so please help ..
This is Vultr's DNS setting and Route53 setting (I have changed the sensetive info)
I believe the issue here is you are attempting to add the Vultr Nameservers as NS records in Route53. So, Route53 would still be your primary nameservers.
Instead you want to specifically change over the primary Nameservers / glue records (separate UI / settings area than DNS records). See the final section on this page for details on how to do this -