🧩 Add new `myst templates start` command to start site templates

[agoose77]

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This PR closes #2017 by adding a new myst templates start command. This command enables using MyST locally to preview remote builds.

It also performs some refactoring to split out the site template serving.

@rowanc1 I did this on the plane, so it might be "I'm sitting next to a really sad infant and it's impacting my decision making skills".