In 50 years experienced by the explorer inside the ship, at a more "realistic" speed of 0.9c the ship would travel ~115 light years, and at 0.99c it would do ~3

In 50 years experienced by the explorer inside the ship, at a more "realistic" speed of 0.9c the ship would travel ~115 light years, and at 0.99c it would do ~350 light years (excluding gravitational time dilation). Anything higher than that would probably be a bit incomprehensible for the human mind. At 0.99999c the ship would travel ~11000 light years, all of which would be fully experienced by the people at home. That's for the dash, the exploration itself comes on top of that. And while at the speed of light time passes infinitely slow for you, it passes infinitely fast for the universe, which would very abruptly end your exploration. We will not be exploring any significant portion of our galaxy without rewriting our current theory, inventing a game changing technology, or maybe discovering some phenomena.