What are some inexpensive DIY options for fixing a low water pressure condition in a toilet?
The immediate non-flush nature of your problem, as depicted in the video, indicates (to me, anyway) a very local obstruction, as in the toilet trap itself. You need to run a toilet auger (see pic) down through the toilet trap and/or pull the toilet to see if there is an obstruction immediately below. This could be anything from packed paper to packed solid material to a kid's toy to rocks from a fish tank. I have seen all those things and more.

If the sewer system itself were backed up such that there was water/waste all the way up to the toilet trap itself, your toilet bowl would overflow onto the floor when flushed and you would very likely have water coming out from under the toilet due to wax seal compromise.