Why is my toilet flushing slowly and not emptying the waste from the bowl?

Had this same experience with a rear-mounted toilet, where the plumbing line entry is on the wall instead of on the floor. The flushing power works different on rear-mounted toilet that the more popular floor mounted. Snaking and/or letting the clog sit a little like overnight etc. did help, but after several attempts, I learned the only way to keep this from happening appeared to be; to get used to hold the lever Down for a few seconds at each flush. that helped.

I recently updated the toilet in my 1930 farm house. I have found a similar problem if I don’t hold the lever down until the tank is empty. It will flush a few times and start plugging up again. I have found running water in the sink and tub helps break up the clog , I am guessing that the old cast is catching some of the paper or waste it builds up and not a solid plug it can be removed with aggressive plunging. I figured out that the water helped the plunging action when I could hear air being sucked into the drains. Running the water gives me more pressure with the plunger and has worked well. With me and my wife holding the handle down we have not had it plug even with a house full of grand kids, see if you can get it to clear out by plunging with water running in the other drains then start holding the handle down when you flush until the tank is empty, if this doesn’t work there could be problems with roots in the lines where a auger with a cutting head may be needed, or even the pipe collapsing. I hope the water and long flush solves your problem.

It sounds like the clog is far enough down so that, given enough time to let the water drain out, there is enough room for one flush to enter the pipes fully before hitting the clog but not for any subsequent flushes.

Like Nate suggested in the comments, your best bet is to snake it. Here is a how to: https://www.wikihow.com/Snake-a-Toilet