AFAIK,
The only way to have this flexibility is using ClientID & Secret
or Service Principal certificates
and each application manage their own credentials.
Service Principal Certificate is already integrated to AD, but does not require the application, the user or the Host to be part of the domain, the only requirement is setup an user on AD to grant the permissions on Keyvault.
There are other solutions using AD integration, like Managed identities for Azure resources(Former: Managed Service Identity) but I am not sure if you are able to restrict access per application like you described, because the MI add this as a service in the node, so technically other applicaitons would have access as well, worth a try to validate if you can restrict this.
If you want to try this approach, you can use with Microsoft.Azure.Services.AppAuthentication for implicit authentication of the services running in your cluster, where the nodes are setup with Managed Identities extension like described here.
Something link this:

When you use the Microsoft.Azure.Services.AppAuthentication, the Step 2 will be handled by the library and you won't have to add much changes to your key vault auth logic.
When you run your code on an Azure App Service or an Azure VM with a
managed identity enabled, the library automatically uses the managed
identity. No code changes are required.
The following docs describe other options you can use for KeyVault Authentication.
PS: I've done other KeyVault integrations using Client Secrets and Certificates and they are secure enough, With Certificates you can store it on the managed store or with the application, I would recommend MI only if is a requirement for your solution.