@Switch BlaydeI decided to ask ChatGTP. The sentences I gave it weren't exactly like the ones in the OP. Here's what I copied from ChatGTP (my question and its answer). I was right about the tense mismatch.
"My first and second houses had pools. But my third house and my current house only have community pools."
is understandable, but "third house and current house" creates a tense mismatch because "have" applies to both.
The clearest and most natural version is:
"My first and second houses had pools. My third house had only a community pool, and my current house has only a community pool."
Or, if you want to emphasize the contrast:
"My first and second houses had private pools. My third house only had a community pool, while my current house only has a community pool."
That second version is probably the best if you're telling the story of your houses chronologically.