I wash and oil my pre-filter and blow the filter clean and reuse it for several years without a problem.
I think you filter was so dirty it caused it to run real rich fouling the plugs.
After you cleaned the filter if you had changed the plugs it would have run fine.
I clean and oil my pre-filter regularly and the main filter stays clean allowing me to use it for several years.
The filter in the Honda is a flat pleated paper filter, much like the air filter in many autos, that fits in a housing on the side of the engine. The prefilter is just a thin sheet of foam that lays under the paper filter. The prefilter is designed to be dry. If it was oiled it would just soak into the paper filter and, most likely, clog it.
The air filter is designed to trap dirt before it can get into the engine which it apparently does well. It appears that at least some of that dirt is trapped well enough that it cannot be blown back out and the filter eventually becomes restricted to the point where the engine cannot get enough air to run properly. I now understand the need to periodically replace that paper filter in order to keep the engine running at it's full power.
Your filter may be designed to have an oiled prefilter but that does not appear to be the case here. I think that replacing the paper filter, even at the inflated prices that they are going for these days, is my best option with this engine. It has been extremely hot and dry here, especially this year. That is causing much more dust than normal, which can be expected to shorten an air filter's useful life. The engine being low mounted in the rear of the mower certainly doesn't help matters.
Thanks again for your input.
Bob