Automated pizza oven, a big no, a proper wood fired pizza oven and barbecue on the roof, yes, he can use stone from the Demonreach lighthouse and create a shrine for the Little folk, a cathedral for pizza. Build a back boiler. The rest can go as a roof top garden, for Maggie and Mouse. Perhaps grow a few tomatoes, onions, peppers (mushrooms in the basement) and a token stand of celery.
A computer could be powered down and only powered up inside an active magic circle, you could have conduits running through the floor, this would allow third parties to use it. If Harry wants to use technology, (and with Maggie he may have no option) he needs to build a personal suppressor device like Thorn Manacles but rather than cut off entirely all magic, just needs to scale it down so he can still use some magic but still use technology, perhaps have it so he can set it from 100% magic to 0% magic and points in between. Similar devices would be for other wizards apprentices in residence. It makes sense to do something like this rather than build it into the Castle, as Harry isn’t always in the Castle.
There was guest accommodation in the Castle originally so if Harry is taking in other wizards and apprentices this could be used for them, but younger apprentices would be better off with the Carpenters initially.
Harry needs a gym himself, but perhaps not the large one. Day care was run from the Castle, so a proper day care centre for Paranetters and SI kids (Bradley needs new daycare).
The Great Hall is a flexible space, suitable for lectures, functions and a variety of events.
Harry I expect will take the much larger basement for his accommodation to create a larger version of his original apartment, two bedrooms, proper bathroom and kitchen and a larger general space