OK, that’s interesting. I wouldn’t really trust to google books since it is OCRed.
I can’t get Google results like those with numbers on mobile, as far as I know. What comes up for me is discussions about what is grammatically proper in this case. https://www.quora.com/Which-is-grammatically-correct-check-i... for instance. All I had to search for was the phrase “check into hotel“, and the results show this is a hot topic of grammatical discussion because that is what came up rather than information about hotels.
‘Check into’ sounds different than ‘sign into’ to me, probably because few say sign vs check for a hotel. I suppose grammatically they’re the same.
I would certainly flag it when editing. I also do not commonly see anyone use the contracted form for this. The reason is that the verb is the phrase “sign in”. The word ‘in’ is not a candidate to be modified by being combined because it is paired with ‘sign’. We would never modify a single-word English verb by adding a suffix like ‘to’, and the same rule applies for phrase verbs. Beyond that, I’m not a grammar expert, so I would imagine the above link could shed more light than I can.