Refactor internal TA service clients to define fewer bespoke methods

[heaths]

While working on #28067 I found that both Analyze Actions and Healthcare Entities were almost exactly the same but had bespoke methods on the ServiceClient abstract class. In PR #30436 for the aforementioned issue, I made more general methods that should probably work for both Analyze Actions and Healthcare Entities with minimal changes to Transforms (see the PR for examples). Apart from making truly generic methods - which I started but ends up being a more complicated call pattern and may be more difficult to maintain as new people are onboarded - what I did in the PR seems like a good compromise: REST calls are general purpose, and anything used by, say, operations deal with specifics, and those specifics turn out to be very little. IMO, this should be easier to maintain.