All in all, everything during gameplay feels "weak". Your own shots, the enemy shots, the ships and even bombs feel weak. It feels lifeless.
I'll just give my feedback in a listy way because I'm lazy
-Control settings. This game is not an arcade game, and the vast majority of players never tap the shot button if there's an option for rapid fire. Therefore, you could re-name the control settings to "Shot, Focus shot" or something instead of Rapid-fire and Fire. Not only it causes confusion in newcomers, it caused me having to remap all buttons multiple times to get it right. Also, remove any transition delay between switching between shot <-> focus during gameplay.
-Prevent enemies shooting from OUTSIDE of the screen and from behind the player. Play around with the values, but something like this:

-Add sound effects to enemy patterns (some visual effect for spawning bullets would be nice too) and adjust the sound effects of explosions to be more energetic. (The enemies before stage 1 midboss sound like farts)
-Some screen-shake here and there when you destroy a big enemy, and make the explosions either bigger or do the usual white-big-circle flash for a frame or two at the start.
Sometimes the explosions are smaller than the exploding enemy itself, making it look awkward.
-There was some dead air if you killed things too fast in stage 3; add enemies to some places that only spawn if the screen is empty (like i think you already do at stage 1 midboss).
Heck, if you wanna be like CAVE, you'll spawn another huge enemy of the same type if the player kills the first one too fast. (like this)
-The shot select screen looks kinda bad, but I think that it's heavily WIP (like everything else lol), but the special weapon select looks SWEET.
-Some bullets could be bigger, like the fast, tiny aimed bullets that the tanks shoot.
-Make medals spin faster
All in all I think I should say that when you're making a shmup (or any game IMO) and implementing features and things, you should first make everything EXTREME. Make visual effects huge & flashy, make sound effects really piercing and loud, make scoring completely bonkers, make gauges/bars increase and decrease really fast, make player movement speed fast etc. and then tone it down over time, instead of making everything lenient first and then adjusting these things up. Of course, keeping the style coherent while doing this is hard, but because of the simplistic nature of shmups you should always maximize the energeticness WITHIN your chosen style-canvas.
Always imagine that someone is looking at your game and thinking "this looks lame" and you want to prove him wrong.
(As an example: Stage 1 midboss warning signs, you could make them flash on-off a few times in order when they appear and disappear, making it look like a wave. Also make them twice as big)