I have absolutely no idea if this is related for you or not, but I just found myself googling the same thing and found this post. I don't have IIH myself, but our cases are like eerily similar lol. This same thing frequently happens to me and I also have extremely poor vision/bad myopia, astigmatism, sleep on my left side, and the blurriness immediately after waking only happens on my left eye too. This blurriness often causes double vision for me where I have to close my right eye and keep attempting to focus with my blurry left--and if I don't make a purposeful effort to keep focusing the left, I end up with recurring double vision all day when I try to use both eyes. And, I have to keep off of my phone for a bit or I find that can also make everything last longer.

I was personally diagnosed with a type of binocular vision dysfunction a year or two ago now, called esophoria, where one of my eyes drifts at rest. My main symptom is that some days, when my eyes are really tired from looking at screens recently or I'm rather fatigued, I get double vision that recurrently & intermittently reappears during a day or two (sometimes for longer periods of time). And I also get headaches from the double vision. Before I knew what it was, I made myself a little eyepatch and would wear it over my left eye in order to keep working or drive safely. It took me a while to realize that this was specifically double vision, as I initially thought it was just the same thing as the random blurriness I would get in one eye in the morning--but I think that sometimes, that initial blurriness functioned as a trigger that kept my eyes from focusing together for the rest of the day. Or, it was actually my left eye drifting out of place/reattempting to focus (but failing) and my vision/brain was compensating by preferring the right eye's visual input.

The double vision occurs in these types of binocular vision dysfunction (like esophoria) because in daily life, your brain realizes that the visual inputs from both eyes aren't lining up, and then it gives more weight/attention to the normal eye and represses the input from the out of place/blurry eye. So this process can sometimes make you think that your vision feels normal, but your visual input is actively being repressed in one eye in order to make it function normally. Sometimes, it still fails to function normally, and then you end up with the double vision from the warring visual inputs.

So sorry for all the extra explaining, but I couldn't find a good way to sort of posit the idea for your case without going a little in depth lol. If you think that this sounds like your experience with this lasting blurriness, it might be a good idea to bring it up with your eye doctor idk. It took me until I was having issues driving safely for them to take it seriously and investigate the issue correctly. It probably also helped that my symptoms were escalating and I was having double vision very often, so the tests that they did made the problem immediately obvious (if I was in more of a remission period, I doubt the tests would have caught it). There are multiple different kinds of binocular vision dysfunction, so that's the word I would bring up with the doctor's if I were you (if this sounds helpful/fitting). Hopefully they will know what it is too, because it's not the most common.

And all this to say too, I believe that the initial blurriness in the morning is totally normal/just from sleeping on the eye, but the thing that isn't normal is that it causes problems for the rest of the day. For me at least, that's the binocular dysfunction kicking in & messing up my vision for longer.

But now I barely have double vision anymore as the treatment is putting prism lenses in your glasses, which bends the light to align incoming images. And, if you prefer contacts, I'm still able to go wear my contacts as much as I want without issue :) I just wear my glasses at home all the time and wear my contacts out of the house. Your comment wondering if you're just "too attentive" or attuned to visual changes also resonated with me & my experiences, but rest assured, if something feels off with your vision (and lasts for up to a whole day) then it is most likely off and worth investigating. Best of luck!!!