I just tried the demo, and figured I would offer a few thoughts.
1. The ship's hit box is very large, even for a game that's targeting the PS1/Saturn era as its style. It almost feels like it's larger than the ship itself, which feels bad when you aren't even grazing an enemy or projectile, and you get taken out. I'd suggest cinching that up a bit so that it's at least the sprite itself only, or perhaps a little smaller.
2. The initial shot type feels very weak, especially against the initial batch of enemies that take several shots to kill. By contrast, when I got the boss and obtained a laser weapon, even though it still took a bit to take out the boss, that weapon felt way more powerful. The weapon system also seems a tad esoteric. That might be what you're going for, which is cool. It's just not super clear what the upgrade paths might be, so I would say keep that in mind as development progresses.
3. I love that you're channeling the Einhander vibes with this, but I'd caution against going too hard in that direction, lest the game gets labeled as little more than a copycat. But the 1st stage here feeling a bit like stage 2 of Einhander was a nice atmospheric touch, and certainly something players of my age bracket will appreciate.
4. On a minor technical note, when I was done with the demo and entering my name in the high score table, no matter what button I pushed to select "OK" in that screen, it never actually selected OK, it just went back to name entry. It wasn't until OK was highlighted and I hit the Enter key that the score saved. I've seen this in a couple other games, and your score table looks exactly like those, so I suspect it's something inherent to the engine you're using to create the game. Still, good to be aware of this as the game progresses.
All in all, this is a solid start with a lot of promise. I look forward to seeing where you go with it!