> and the best the algorithm could do will be limited by the uncertainty in estimating those values

That's relatively easy if you're assuming simple translation and rotation (simple camera movement), as opposed to a squiggle movement or something (e.g. from vibration or being knocked). Because you can simply detect how much sharper the image gets, and hone in on the right values.

I recall a paper from many years ago (early 2010s) describing methods to estimate the camera motion and remove motion blur from blurry image contents only. I think they used a quality metric on the resulting “unblurred” image as a loss function for learning the effective motion estimate. This was before deep learning took off; certainly today’s image models could do much better at assessing the quality of the unblurred image than a hand-crafted metric.

Record gyro motion at time of shutter?

Just guessing, patent troll.

I wonder if the "night mode" on newer phone cameras is doing something similar. Take a long exposure, use the IMU to produce a kernel that tidies up the image post facto. The night mode on my S24 actually produces some fuzzy, noisy artifacts that aren't terribly different from the artifacts in the OP's deblurs.