I have created a few B2C directories using the classic Azure portal. Sometimes it adds the b2c-extensions-app but other times it does not. When I delete a directory, Azure seems to have a long memory which prevents me from trying to recreate it (with the same name).
Is there a way to manually add the b2c-extensions-app such that it shows up under "Applications my Company Owns" listing?
The b2c-extensions-app is created automatically as part of creating an Azure AD B2C tenant. It should always be created. If you create a new tenant and this app is not present, you should open a support case so that the Azure AD B2C team can look into this.
More likely, someone accidentally deleted the application. If that's the case, there's two options:
Notice that it's available in App registrations:
NOTE: Make sure you pick "All apps" from the App Registration drop-down.
But not in the B2C Applications: