Still not fully getting Bitcoin… What’s the real long-term value?

I've got a CS background and love blockchain as a technology. I also love the idea of Bitcoin and have recently started DCA. But I'm trying to wrap my head around the economics of it... I was hoping someone could help me with my concerns:

1. I get that Bitcoin’s value is store of value like gold — than being a productive asset. And sure, gold isn’t productive either, but it’s also a relatively poor hedge against inflation historically. So is Bitcoin’s value proposition that it's a highly undervalued form of digital gold that will eventually reach its intrinsic value and then grow more slowly, like gold does? If so, how do you determine what that intrinsic value is?

2. Bitcoin’s day-to-day transactional use seems limited. I understand that layer 2 solutions (like Lightning) address these issues. But if most people will interact with Bitcoin through these layers and exchanges, isn’t that essentially replicating the existing financial system? Does Bitcoin become redundant unless you don’t trust the current system?

3. I often hear Bitcoin described as a hedge against governments, central banks, fiat collapse, etc. That makes me wonder: if you do trust the financial system (for now), does that significantly diminish Bitcoin’s value proposition? Is it only a strong asset if you believe the system is broken or will eventually fail?

4. I get that Bitcoin has a fixed supply, but it’s also infinitely divisible, and most people buy in fiat-denominated amounts, not full coins. If we can keep slicing it smaller and smaller, why does scarcity matter so much? What mechanism ensures its price goes up in the long run, beyond just people continuing to buy more?