I understand that you would like to register a domain with .app TLD on AWS however, you were unable to find it. Below is my observation on the same.
Unfortunately, as of now .app TLD is not supported on Route 53. Here is the list of TLD that is supported . However, as a workaround you can still choose Route 53 as your DNS service provider for your .app domain registered with a different domain registrar. Refer  for more details on how to use Route53 as DNS service provider.
AWS does not have a timeline when this domain extension will be added to supported domain names, but you can check it periodically to see if '.app' domain names are available by reviewing this AWS documentation.
Additionally I do encourage you to keep in touch with the community pages (What's new page or AWS Blog) so that you know when it does get implemented .
I hope this information will be helpful. Feel free to reach out if you have any further queries or concern.
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