Submersible experiments around the age of Turtle

Did other navies experiment with devices like Turtle during the American Revolution?

Yes; British and French officers and inventors explored related ideas, often privately rather than through clearly documented official programmes.

Other experiments with submersible ideas were taking place around the American Revolutionary War. British and French naval circles both examined related possibilities. Much of the work could be private, with officers or would-be engineers building and testing devices on their own initiative. Results might still reach the Admiralty even when the service itself had not formally sponsored the trial, making the historical record harder to trace.