When is one preferred over the other?
This is in the context of the door to a large room. My sense is that "into" is preferred for closed spaces and "onto" for open spaces. This situation is kind of on the cusp.
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These Google ngrams, for
support the sensible explanation you put forward.
Of course, there are 'the doors are open into the garden' and 'the doors open into the garden' tokens commingled in these results.