Good question - thanks for asking it. The object of the site is to collect answers to (on-topic) questions for future use.
I would recommend a variation of one of your options, namely:
- Post an answer with "I improved the circuit as mentioned in the comments as follows" and include a summary of your improvements in the answer. You can then accept your own answer, to effectively show that the topic is closed.
There is no point in an answer which effectively just says "fixed it" (in different words). But an answer which includes how you fixed it, and especially if you can specify why a particular change fixed it, would have value for the future.
One concern: You say that you have a new question. Before writing an answer saying that changes XYZ solved your problem, we need to make sure that your new problem isn't a different symptom of the same problem, meaning that changes XYZ didn't solve the problem. So is it premature to write an answer to your old question, or are you sure that your improved circuit has really solved that original problem?
Summary: If there is a way to capture knowledge in an answer, which can be used for the future, we should try to do that.