Interesting. Have you applied SR to an HR image? Or just AI sharpening?
I've not applied Lightroom's Super Resolution to Panasonic Hi Res images. This is a step too far for me and not what I'm interested in right now. Also Lightroom doesn't have AI sharpening per se.
To clarify this, the AI Detail section in Lightroom has three available functions: Denoise, Raw Details and Super Resolution. Denoise and Super Resolution are trained with gillions of images, just like the Topaz applications (and like the many other AI photo apps). Denoise obviously reduces noise, and Super Resolution doubles the number of pixels in both the X and Y directions. A 6000 x 4000 24 MP image becomes a 12000 x 8000 96 MP image, with AI processing filling in the detail it remembers from the gillion other images. Raw Details is somewhat different; it is an advanced demosaicing algorithm that converts the RAW Bayer sensor data with more detail, again with the AI training. By itself it doesn't show much if any sharpening effect. Raw Detail can be used by itself but usually in conjunction with either Denoise or Super Resolution, but not both of these at the same time.
Lightroom had major upgrades for these functions in the middle of 2025. They are now non-destructive and reversable, and no other files are created, so they work like the other tools in Lightroom. That is, they are easier to use and you can experiment and change your mind.
My limited experience is that Super Resolution with Raw Details gives high resolution results as good as, and sometimes better than, Panasonic Hi Res (including with high ISO noise). This is with the S1II - I've not looked at this with the S1RII yet. The Lightroom advantage is that Panasonic Hi Res doesn't do well with motion in the image. Also for me and my non-stable hands I can't get good hand held Hi Res results, so Hi Res only works for me with a tripod. The Lightroom approach doesn't care about motion - run up shutter speed and you are good to go, so it is much more useful than Hi Res.
I use Crop Zoom quite a bit. This makes any lens more versatile - with the CrZ function assigned to the lens focus ring you can use it like a zoom ring to frame any shot. On the S1RII I limit this zoom to 2X, and on the S1II I limit it to 1.4X. And Super Resolution lets you easily get back the pixels lost with CrZ.
Back to your question, could you use Lightroom Super Resolution on top of Panasonic Hi Res? I expect someone will explore this and get nice 707 MP images with the S1RII, but in my case Hi Res is too limiting so I'm not very interested.