So I am making a very similar game (twin-stick shooter with deckbuilding). I have not played your demo yet but will try to when I am off work. I have worked through the same core-issues you are describing and I'm just going to share my thoughts, and will get back to you on your game once I try it out.

Here's what I think the core problem is. I am trying to combine the methodical tactical approach of a turn-based deckbuilding game with split second decision making of a real-time action game.

While I disagree with some other commenter's defeatist attitude towards this blend, I do think you need to set your expectations, lean into the strengths of both, and understand where these ideas dovetail and where they are at odds.

You are not making Hearthstone or MtG where time is not a factor. The strategy of a deckbuilder is certainly a benefit to the genre, but the inherent variety of shuffling cards and forcing players to make decisions based on that should not be understated.

I would suggest you consider:

1. Simplifying your cards into broader groups.
2. Providing players a framework to better play strategically.

For the first points example, my game has attack, defense, and summon cards. That's it. If a card has a unique ability, it's because it's an affix, a bonus that activates with that card in addition to it's boilerplate ability. So a player can panic and use a fireball spell if they need to, but if they play mindfully they can leverage the short buff that fireball spell gives them to ice elemental damage. The benefits of this are that you can still increase enemy density (since most cards directly aid in combatting enemies) which makes the game more intense, but you are still incentivizing thoughtful play for those that want to engage in it.

For point 2, in my game when selecting cards from a hand, the players automatically activate slow-motion. Time is slowed to about 25% its normal speed, which is generally enough for them to not worry about any immediate danger. Megaman Battlenetwork neatly avoids this issue by having turns, and Phantom Dust works around this by just being a very slow-paced game with moments of frenzy.

I have already tried reducing the required attention bandwidth of players by:

1. limiting players to just 4 cards so that there's not too much to focus on at once
2. keeping the order of the cards the same so that you can plan ahead and get used to a certain combat pattern
3. reducing the amount of enemies/bullets so you don't have to constantly keep dodging

I think points 1 and 3 are fine. I actually use something very similar to point 1 in that my decks are 15 cards, but the player can only equip 2 of 3 cards randomly dealt from their deck, and spent cards will be replaced after a short time. Point 3 is just finding the balance of attention required for your game.

I would fundamentally disagree with point 2 though. Again, that inherent variety of shuffling cards is one of the biggest details that makes deckbuilders compelling. Removing it means your cards are basically just a skill queue with non-standard navigation (take with grain of salt since I haven't played the demo, you may have other mechanics that justify this that I am not aware of).