[Discussion]: Update and periodically test posts and model-zoo tutorials

This is a placeholder issue for updating the existing tutorials and adding workflows to periodically test them.

My proposal's text -

> Flux's website has plenty of good tutorials, but some of them have been outdated for some
time. These tutorials go stale with every new Julia and Flux release making them unreliable
for newcomers. Additionally, as discussed with Dhairya Gandhi, the FluxBot can be used to
automatically test these examples, but it is currently not integrated with the FluxML
ecosystem. The bot would ideally run all the model-zoo examples on every PR created on Flux.jl.
This section would aim to -
> - Update the tutorials on Flux’s website.
> - Add tests to (or run) these examples to ensure they do not go stale.
> - Integrate FluxBot with the existing FluxML ecosystem and get it running.

I tried triggering the FluxBot (https://github.com/FluxML/Flux.jl/pull/2016#issuecomment-1207408307), but it did not respond. I am guessing that the bot is not deployed at the moment. I did find a buildkite-related file and a PR (https://github.com/DhairyaLGandhi/FluxBot.jl/pull/2) that probably aims to shift it to GitLab's CI, but I am not sure how and where it is deployed currently. I am also not sure if there is a way to run it locally for some personal test repositories.

For the tutorials, should I migrate them from `Flux.params` to `Optimisers.jl`, or would it be too soon? I will audit all the tutorials and update them as needed!

For testing, I think it would be straightforward to periodically test the model-zoo examples using Julia's doctests, as model-zoo is a Julia package. For the website, I think the -
```
doctest(source, modules; kwargs...)
```
definition of `doctest` should work.

Also, #136 aims to migrate this website to `Franklin.jl`. Is this still in progress or has this been abandoned? I can take this up if required (cc: @logankilpatrick @darsnack)!

I will start by adding these periodic tests to both the repositories!

cc: @DhairyaLGandhi @mcabbott @ToucheSir