What you are looking at is just an implementation detail that you really don't need to worry about. It's just converting from an internal format (which may use different coordinate systems and bit lengths, especially for tests) to the standard output format. Within the library itself, the data in the signature may be easier and more efficient to handle when in other formats or coordinates systems. So the structures that represent that data store the data differently. However when outputting results, it must all be in a standard format, so that's what these conversions do: change from internal representation to a standard output format.
This is done for any of the signature serialization outputs that libsecp256k1 does. The compact format is just the two 256 bit values for R and s concatenated with each other. The first 32 bytes is R, the second is s. For standard compact signatures, that's it. For compact recoverable signatures (which is what you are looking at), there is an additional byte for the recovery id that is prepended to the compact signature.
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