Personally, I'd just keep cooking with it. I wish someone had told me that when I was getting started with carbon steel. In my experience, keeping the seasoning visually even across the pan is much harder on carbon steel than cast iron. I was restarting constantly because it would look splotchy, but eventually gave up on that. As long as it performs fine and there's no rust, there's nothing to worry about. Eventually it'll all even out.
This sentiment is worth spreading. Cast iron pans were around long before anyone knew what a polymer was. You can get a -good- seasoning coat from just regular use. Active seasoning can give you a -better- one, but pans have lasted decades and generations on just the seasoning gained from cooking.
You're fine enough. Might need to restart, but I've seen pans in worse shape recover fine through regular use. Mind you, it won't be as low-stick as if you scrub it down to metal and reseason, but it isn't necessary.
This is what mine looks like after washing it out with a chainmail scrubber and soap and water. Just do a couple quick seasoning layers on the stovetop with high smoke point oil (avocado, grape seed, etc) and a paper towel to get the layers on as thin as possible.
yes and no.
it'll be fine if you continue regular use. heat slow, oil well. then dry well, protect with a very light coat of fat. a single drop is enough to oil the whole base. test w
with your finger, if it feels oiled it's oiled.
If you are really obsessed with getting a perfect finish then you could but i would just make sure no rust, put a bit of oil and keep cooking or heat up with the oil to put a fresh layer on the bottom if im feeling like it.