What’s the difference between a gaussian stan_glm and stan_lm? Is it just the priors? Is there anything online I can peruse? Do they both use Hamiltonian MC?

There is a vignette for it (and most other things) https://cran.r-project.org/web/packages/rstanarm/vignettes/lm.html
Everything in rstanarm uses Stan’s default MCMC algorithm (which is NUTS rather than HMC with static integration time), unless you specify the algorithm argument differently.

With this much data and so few predictors you are fine with normal prior. For faster inference, it’s likely that you get practically the same accuracy with algorithm=“optimizing”. There will be soon a function implementing diagnostics for this.

launch_shinystan is going to take a long time since it has to do posterior predictions for all observations. If you look at the help file, there is some way to make it skip that but then it is less useful.