A single neural network could be made report the class assignment probabilities instead of just the most likely class. And a model that provides a single numeric answer could report a SE. But a LLM gives you a complex response. How to report a CI for a long textual response?

It really depends how you count. Is GLM a single method or many? But among univariate distributions, t is probably my 6th most frequenly used, after normal (including lognormal), gamma (including exponential, chi-square and inverse gamma), uniform, binomial (including Bernoulli) and Poisson.

I did things like that when working for an in-play sports betting company. Not shooting but e.g., darts.
We have a beta prior for a given contestant's target hit frequency in this event, informed by his past performance in similar events. Then we update this using his history in the current event.