There has been some confusion about this question: https://www.thewisedrive.com/turn-signals-in-dedicated-turn-lanes/ https://www.thewisedrive.com/yes-you-have-to-use-your-turn-signal/ https://www.clickorlando.com/news/local/2023/12/26/watch-live-trooper-steve-explains-whether-you-need-to-use-turn-signals-in-turn-only-lanes/

I think the idea of a “direct course” is useful:

No person shall turn a vehicle at an intersection unless the vehicle is in proper position upon the roadway as required in RSA 265:42, or turn a vehicle to enter a private road or driveway, or otherwise turn a vehicle from a direct course or move right or left upon a roadway unless and until such movement can be made with reasonable safety. No person shall so turn any vehicle without giving an appropriate signal in the manner hereinafter provided.

I do pay extra attention to giving a signal when I intend to make a U-turn rather than a typical left turn.