Any impact from the client side / Application perspective if the developer edition is used in the Non Prod environments.
No difference.
Any features missing unavailable in developer edition compared with enterprise edition.
Yes. Developer Edition is limited to a single Distributed Reply client. However, this will not impact normal development and testing since the feature is used only for replaying workloads from captured traces and not often used. The feature is not included with the SQL Server 2022.
If The application connectivity to the SQL database(Dev edition) is Public IP and it is facing the internet. Then there is any impact? If yes, what is the impact.
Exposing a database server to the public internet is a significant security risk regardless of Edition and should be avoided when possible. Extra measures (hardening security at all levels, client IP whitelisting, non-standard port, strong passwords, etc) should be employed.