I used to shoot with two identical FF cameras with primes so I could effortlessly switch back and forth. As a pro, it was also easier in post-processing so that both cameras produced identical images.
However, in a non-pro situation where your income is not dependent on a backup camera, the KP makes more sense to me as a lighter, faster fps, crop sensor camera with a built-in flash. With the money saved, you could eventually upgrade your K1 to the K1 II.
However, in your original post, you do mention both the K100 and KS1 as less used due to difference in ergonomics from your K1, and certainly the KP without a top LCD window and a different front index finger wheel will take getting used to.
So, the conservative answer is to get the K1 II unless you just wonʻt take with you a second body because of the weight. The KP makes the most sense if you really need a lighter option that is replacing the dying KS1 and old K100.
Pentax KP vs Pentax K-1 Detailed Comparison
Make a pros and cons list like the link above, but with your personal priorities. Highlight the top three considerations (or more than three, but make it an odd number) and see where the chips fall. Let it sit for a few days and then look at your list again.