Just to reiterate your point, equity is a holding in an asset, at cash value, which isn't yet realised. This could be part ownership of land, or shares in another company. It's not at immediate disposal and isn't a "reserve" like in the traditional sense. In this case it's the Net Value of all of their assets, which includes Cash at bank and in hand.
It would also be remiss to leave out that Paulton's Park also has outstanding, non-cancelable, minimum lease commitments of £16,114,762, as of December 2023, which is almost equal to their entire equity.
And looping this back to the original point, this is also how Merlin operates.
Paulton's Park hasn't created some sort of new lean and amazing business machine. They raise capital against their existing assets, refinance bank loans when it suits them, and the parent company diversifies its portfolio when the park needs additional help. The only difference is that Paulton's Park is doing this for one site only, compared to 130 attractions around the world.