Moving is the category people often define too narrowly. It can include temporary storage, cleaning, utility setup and replacing things that do not fit the new space. Get firm moving estimates, then keep that money separate from the repair reserve.
The phrase “cash after closing” can also be misleading if the full amount is treated as spare money. Property tax, expected fees, inspection items and general repairs are different obligations. I’d list them separately before deciding what remains discretionary.
One practical step now would be...