Hopefully this saves someone else an hour of digging. Philips Hue has a comparison page for their strip lights. This table says that for the Ambiance Gradient lightstrips, “Cut pieces can be reconnected”. Their “Can you cut LED strip lights” page also says “Many strip lights are cuttable, and some even allow the cut parts to be reused and added to the strip light using a connector. Lightstrip V4 and many of the latest models will enable this level of customization.”

Lightstrip V4 has been out for six years, but at least as far as Hue’s official product line goes, the statement “Cut pieces can be reconnected” is not true. Hue’s support representative told me that Hue might someday release a connector which allows reconnecting cut pieces. However, that product does not exist yet, and they can’t say when it might be released.

In the meantime, there’s a company called Litcessory which makes third-party adapters for Hue strips. I haven’t tried them, but I think they might do the trick.