A Brita filter =/= a survival straw. There ARE filters you can use to drink directly from water sources in nature that will filter out all contaminants but a Brita ain't one.
Exactly, there are filters for tap water and there are backpacking or survival filters for filtering dirty water. I use both regularly, but wouldn't ever take my filter pitcher hiking.
The majority of LifeStraw products for individual use are microfilters with an absolute pore size of 0.2 microns which remove bacteria, parasites, microplastics, and dirt/silt.
LifeStraw also manufactures ultrafilters/purifiers that, in addition to the above contaminants, also remove viruses. The absolute pore size on these purifiers is 0.02 micron.
Sawyer filter inline with a camelback is awesome. I'd just fill up my camelback in a stream using a (clean) handkerchief to get the large debris out and then let the filter do the rest.
The most common cause of symptoms like in OP’s story are multicellular organisms. While still microscopic, they are plenty large enough to get caught in a filter. The filters are usually good enough to catch bacteria too.
They clog and you do need to rinse them, and running (clean) water in the opposite direction is a common way to clean them.
They do eventually degrade or clog to the point of being unable to function and then you have to replace them. Usually they fail such that it gets slower to filter the water rather than letting dirty water through, although that’s not always the case. One time I had a cracked filter, and the symptom was the filtering went suspiciously quickly. I think I drank some only partially filtered water before I figured it out (didn’t get sick though).