Your search attempt was doomed to failure.
For one thing chat.db is a SQLite database file unreadable outside of SQLite. There are three files in any SQLite database .db-wal, .db-shm, and .db and you have to have open all three with SQLite in order to extract any meaningful content from any one of the three. There are numerous SQLite database files used throughout equally numerous macOS apps and utilities. So files with the .db extension can belong to Photos, Music, webkit, Weather, Safari, as well as dozens of other third party applications. Safari alone has three or four .db databases. Therefore there is no way for Finder to determine which application any given .db file belongs to, so it doesn't even attempt to open anything.
QUESTION? Why didn't you use the search function in Messages?
As far as why Go To Folder… would not open ~/Library/Messages, my suspicion would be a typographical error.
