Jackson Cannon’s favorite bar tool is a Hawthorne strainer. The tool is distinguished by its springy wire coil, which fits snugly into the top of a mixing glass. He likens it to a saxophone: It was around long before the world went electric, yet it’s still a very specific, useful, modern instrument. “It’s nineteenth century technology, and we still use it,’’ says Cannon, a co-owner of The Hawthorne, the new bar in the Commonwealth Hotel’s semi-subterranean space, formerly occupied by the Foundation Lounge. It opened this week.