Reginald Barclay may have originated on The Next Generation, but he clearly suited the tone of Star Trek: Voyager. First appearing in the second season, by the end of the series he was a defacto member of the crew, going so far as to establish regular two-way contact with the lost ship.
Barclay is a clear stand-in for the underdog character in Star Trek. This much was evident on both shows he appeared on, but it was with his Voyager family that he flourished. Now that Star Trek: Prodigy is exploring the period of time after Voyager's return to the Alpha Quadrant, with Admiral Janeway in command of the USS Dauntless, it makes sense for Barclay to join her crew as her techie.
In a role that might prove similar to Oracle in the Batman universe, Barclay may not be the bravest of souls when it comes to physical combat. However, his innovations paved the way for distant contant. With the Dauntless en route to the Delta Quadrant again, he would be the ideal candidate to remain at Starfleet and to serve as a liaison with the ship - highlighting, once again, his importance with the lives and future of the crew of USS Voyager.