I would say it made him feel the opposite of safe, because the re-emergence of affectionate feelings toward Thor was a threat to his ability to carry out his mission! But yes, you could really see how the gesture called up strong associations and memories of their relationship over the centuries.
As for The Neck Thing™ I see what you mean about it having an old culture feel. It’s very intimate, and nowadays men don’t show affection like that (usually). With that being said, they did The Neck Thing in The Avengers, and I really feel like it worked there. I didn’t ship Thorki when I first saw that movie, and I was really touched by how the gesture affected Loki – you could see it in his eyes how much it meant to him, probably because it reminded him of their bond and made him feel safe.
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Loki is the Philosopher King 