Right now, nobody would even notice. Presenting a British passport means you have to fulfil a number of requirements and could in principle be refused entry but that remains rare. Visa-free visits for British citizens are also limited to no more than 90 days in any 180-day period in the Schengen area. This is enforced using the stamps in your passport and not through any sort of Schengen-wide database. Even for British citizens, questioning is typically not very thorough and none of this would have any impact whatsoever on later travel on your Italian passport.
The main drawback is having to use slower “all passports” lanes at border control points but British passport holders are actually allowed to use the automated passport gates at both CDG (or St Pancras) and Schiphol (only when leaving the Netherlands but that's what you will be doing) so you wouldn't suffer from that on this particular trip.
That said, the EU has been working to tighten border enforcement using technology. There are two systems that are supposed to gradually come online in the next couple of years and would impact British citizens:
Whatever happens, your legal position remainds the same. You do not risk a fine or any other serious consequences and will always be able to present your Italian passport to clear any question border guards might have. But ETIAS in particular will make it more difficult to carelessly use your British passport in the future as transporters will need to verify that you applied for prior authorisation. And even if there is nothing illegal about it and no reason it should create problems, any trip on your British passport ought to be recorded in a database for a few years and easier to find that it currently would be.