Yes Dorothy, Kansas does have two severe weather “seasons.” At least most years we do. The Spring season is the one most people talk about when they say “severe weather season.” As shown in the graph below from NWS Wichita, the peak tornado month in Kansas is May. The majority of severe weather tends to cluster into about 6 weeks most years, centered around the middle week of May. (One of the reasons I knew I was born to be a storm chaser is that my birthday falls right at the historical peak of tornado season!) Some years it gets clustered into a couple of weeks, and some years we go from mid-March to early July.

As you can see in the graph, there is another minor peak in tornado occurrence in the fall. Generally we have a 1-2 week season, featuring no more than three major storm systems. The dynamics that cause the seasons at the times they are and for the duration they are are the same both halves of the year. Storm incidence increases as the jet stream undergoes its changes between the typical winter flow and the typical summer flow. I plan to go into that more later this week, but suffice to say the fall transition happens more quickly in almost every year.
What about 2021?
Long-range models are currently forecasting the possibility of a strong system on Sunday/Monday (Oct 10-11) followed by another, potentially stronger, system on Tuesday/Wednesday (Oct 12-13). Here are some graphics from the model runs current as I write this (evening 2021-10-03).
For the first system, Kansas would be along a trailing cold front from a surface low pressure center over northern Minnesota. A strong mid-level low would be rounding the bottom of the flow over the desert southwest and would provide some good wind and instability to help storms grow.

On Tuesday night/Wednesday the push in the mid-levels would be even stronger:

Typical cautions apply to these maps: we are 7-8 days from the earlier event and 9-10 days from the second one. Models are frequently off-base this far out, and time errors can be measured in half-days to full days, while place errors can be measured in the range of half a state.
That said, I felt it a good idea to get the word out early since many people get surprised by severe storms this time of year, especially if we end up having some tornadoes from these systems. We’ll be watching models throughout the week and updating you as needed.