Bringing up games in vague order of most to least Starsector-like:
Starcom Nexus - 2D Space exploration. I found it more puzzle-based and with too much flying around to get to places for my tastes. Build a spaceship with a hex-based grid, exploring a lively galaxy and unlocking more pieces or buffing your ship by advancing the tech tree.
Star Valor -2D, RPG-like combat, but with spaceships. Level up, replace your Light Burst Laser with a Rare LBL for more damage. Currently under development, fleet management is awkward and crew member skills are very roulette based. Can run around trading resources
Reassembly - make a ship out of pieces. Strong modding community.
Cosmoteer - build spaceships out of blocks and fight them. Also watch tiny crew-members walk around carrying things and see their corpses when the ship burns to death. Free demo out which is currently the entirety of the game.
Transcendence - another 2D RPG with spaceships. Downside is that you can't fire more than one gun at a time. Fleet's aren't supported, if I remember correctly.
Three more games that are probably too far from Starsector, but should be noted anyways:
Sector Six - 2D arcade horizonal shoot-em-up with questionable balance choices. Make a spaceship out of blocks and fly through levels. Level up and buy skills. I found it fun, but can see how it would be monotonous.
Shellcore Command Remastered: Based on a series of flash games from the 2000's, this remaster tries resurrecting it as a fan project. Tron-like 2D graphics, assembly a 'shellcore' out of various pieces and fight through a campaign. In development with a very long development cycle. Free.
Istrolid - build spaceships out of blocks, fight through a campaign for more blocks. I ran through the campaign once and put it down. Game is free.