Both your sentences are grammatically sound. The use of since does not affect your choice of tense in the first part (independent clause) of either sentence. Think of them in isolation first:
I have not been going to the gym.
The practitioners have been taking good care of the patients.
Both are perfectly sound sentences up to this point. Now, let's think of since. It introduces a time comparison. Something happened prior to the events in the independent clauses. For this time ordering, you need a "past" tense - not necessarily a tense named past but a tense that describes an event in the past. You have two choices:
- Simple past
- Present perfect
Now, present perfect continuous describes a situation that started in the near past and continues to exist. The doctors started taking good care of the patients and are still doing so. So, both present perfect and simple past can precede situations described using present perfect continuous.
At this point, your question boils down to one of the many questions of present perfect vs simple past. Since simple past is a better "dot on a timeline" event, that would be a better stylistic fit in most cases.
I have not been going to the gym since I came back from overseas.
The "coming back" is a single isolated event that happened before the independent clause. Present perfect is a "section on a timeline" tense, making it less fit as a time marker.
However, this is based on style and idiomatic use, and not on grammar.