Anything you don’t mind upgrading when u get your new pool. It depends on what your budget allows & if you need to sell big ticket items like your dolphin. Perhaps they may be willing to buy it from you.
I would probably leave most all maintenance items/tools especially since your new home doesn’t have a pool yet & you will have to store the items somewhere for an undetermined amount of time. I am also one of those people who sells my vehicles with the custom mats in them instead of removing them & trying to sell them separately so ymmv
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Instructions on how to operate the pool & use the test kit etc. would probably be quite a blessing to the new homeowner.
I know that so many people who buy a house w/ a pool & are left with zero guidance. Then some luckily end up here trying to figure/sort things out. Others struggle for years.