I’ve done that - moved out of a mold infested house into a brand new house and kept some but not all belongings. Can you elaborate on risks? What do I need to watch out for?

I wouldn't worry if you have no symptoms. I'd advise to regularly monitor biomarkers of your immune system (monthly/quarterly bloodwork with vitamin D etc), take approriate supplements which take into account any genetic metabolism defects (MTHFR), and listen to your body, especially the magic tingling of your nose and any symptoms of seasonal allergy.

Generally a DIY HEPA filter and a CO2 monitor should be enough to keep good air in a home which does not have water damage. If you have ventilation then remember to swap your filters.

Mold can stick to some of the furniture even if it's not a large, visible spot. When mold developed on the wall behind your large wardrobe there's a good chance that the wooden back of the dressed caught a bit of it. You move to a new place and carry the spores with you. At worst the new place also has a humidity problem and the spores you brought accelerate the mold development process.

Anything that sat around a mold infested area is something you should look at closely, at least to proactively give it a thorough scrub and dry in a well ventilated area before bringing in the house.

An air filer with a real HEPA filter will help catch airborne spores but if you already have mold growth anywhere in the room you need to take care of that before blowing air all around.

So this might not be the answer you were looking for, but from my digging into this ozone treatments can supposedly kill the mold spores but they are still able to somehow harm you when you breath them in. Mold is one of those things that is supposedly so bad to have around, even when dead in the furniture, can continue to harm you.

We have mold in my family's basement downstairs too and I run the ozone generator a lot to freshen the air. But unfortunately parents would never throw out the things.