Does the word "writes" refers to "sincerely" or "from" in the context?
No, not in this context. They use the word "writes" here because these farewells/comments were written on a social media platform. In news reports, if a news station reports on something that was written on a social media platform, the reporter will say "writes" or "wrote" because it wasn't vocalized. They do this to ensure they are accurate in their news reports.
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