more glm functions

Feature request: glms for positive continuous distributions

It would be very useful to include _glm_lpdf functions positive-only data with positively-skewed errors. (See my post here
https://discourse.mc-stan.org/t/trying-to-understand-glm-lp-f-functions-in-stan/16400/5).

In cognitive psychology and psycholinguistics, reaction (and reading) times are usually fit with a lognormal likelihood. So I think that lognormal_glm_lpdf would be for sure useful for wide audience.
A gamma distribution is also not uncommon (also for ecology, https://seananderson.ca/2014/04/08/gamma-glms/), but here there are several posibilities for a link function, inverse link, no link, log link.

Additions by @avehtari:

• We're missing also binomial_logit_glm (requested in Stan discourse.
• ordered_probit_glm (we have ordered_logistic_glm)

So the current wish list would be

• lognormal
• gamma
• weibull
• ordered_probit
• binomial (added in 2.34 January 2024)

The issue names no files, tests, or entry points and lists lognormal, gamma, Weibull, and ordered probit GLMs, with multiple possible links for gamma. Start by reviewing the existing GLM implementations and resolving which distribution and link combinations are in scope. Done means the selected subset has agreed behavior and coverage.