The one thing you will quickly learn with respect to diabetes is that we are all different.
The correct dose of insulin is the one that maintains our blood sugars pretty much in range.
You have already found out that our blood sugars (and the required insulin to manage it) depends on more than just the carbs we eat. Like you, exercise has a big impact on the amount of insulin I need. That said, my exercise is more than an amble around the park - it is usually 90 minutes or so pushing myself on the bike or, in non-covid times, a workout in the gym or a session on the climbing wall.
The need fro insulin to go away for a while is probably related to honeymoon period - for some time, our pancreas continues to make some insulin. Some times it can have a spurt and produce enough and then, maybe after over-exerting itself, it has a break. This can be a bit of a challenge. I was diagnosed in my mid 30s and my honeymoon period exhibited itself with a continual slow increase in my insulin needs. It had no spurts just a very slow decline. When I write "slow decline' I mean that my insulin dose stabilised after EIGHT years.
So, to answer yours question about whether you may need to stop insulin, the answer is ... maybe.
Keep a close eye on your blood sugars, work with your diabetes team and adjust your insulin dose accordingly.