@Harshavardhan
I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others", I'll repost your solution in case you'd like to "Accept" the answer.
Issue:
When running your python script to get private endpoints for the key vaults, you ran into the below error message.
Error Message:
No HTTP resource was found that matches the request URI 'https://control-.../subscriptions/{subscription-id}/resourceGroups/{rg-name}/providers/Microsoft.KeyVault/vaults/{vault-name}/privateEndpointConnections?api-version=2022-07-01
Solution:
From your error message, you were able to resolve the issue by using the correct Key Vault Private Endpoint Connections - List By Resource API call.
GET https://management.azure.com/subscriptions/{subId}/resourceGroups/{rg-Name}/providers/Microsoft.KeyVault/vaults/{vaultName}/privateEndpointConnections?api-version=2022-07-01
If you have any other questions or came to a different solution, please let me know and I can definitely update my answer.
Thank you again for your time and patience throughout this issue.
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Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.