Therefore I would like to see Milan signing a striker this summer. If they want to play more competitive and consistent for the Serie A title then they need to make some important changes. Origi would stay I assume and Giroud has one year left on his contract. If they find a reliable striker now this can improve their productivity a lot.
Milan needs good transfers if they have a championship goal again. I think they will send Origi contrary to what you said. When Origi's market value is at a good level, they will send it and replace it with a better player. Maybe they can send him without expecting a good fee. Giroud may not be enough for next season. They should get a forward next to Giroud. Otherwise, they will still be behind Napoli. The transfers are not clear yet so I can't predict but Milan definitely needs transfers.
Considering that many players from Napoli will disperse to European teams, there will also be a loss of power in Napoli. To collect this power loss, Napoli have to assemble good players next year, as it did this year. On the other hand, reinforcements are necessary in Milan's offensive zone. Success cannot be expected in all lanes with Giroud alone.