[Parser][NFC] Move `ParseInput` into the parser context (#5132)

Rather than passing both a `Ctx` and a `ParseInput` to every parsing function,
pass only a `Ctx` with a `ParseInput` inside of it. This significantly reduces
verbosity in the parser. To handle cases where parsing needs to happen at
specific locations, which used to be handled by constructing a new `ParseInput`
independent from the ctx, introduce a new RAII utility for temporarily changing
the location of the `ParseInput` inside a context.

Also add a utility for generating an error at a particular location to avoid
having to construct new `ParseInput` objects just for that purpose. This
resolves a few TODOs about correcting error locations, but since we don't test
those yet, I still consider this NFC.

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