I think there are some lead paint test kits with awfully high false positive rates. If you're using 3M's kit, I think that one's notorious for false positives. I'd research lead testing if I were you.

The issue with lead paint is ingestion- do you have kids?

I‘ve always lived in house with lead paint… tbh i’ve never tested although did test myself while living in house while preganant and doing major kitchen reno and still zero.. kids are the real issue as you are not licking the walls…. Pretty common to see non zero lead levels in kids (ie level under 5) that correct after afe 2. things like opening windows will put a tiny amount in air and they eat dirt or whatever. i’ve always been told as long as painted and not peeling its fine.

My DD is a pediatrician and has raised her 2 kids in a home built in 1930. Like the others said, as long as they are not chewing on the window ledges you should be fine.

BUT let the kids doctors know and they will suggest testing occassionally.

If the paint is intact - not peeling, crumbling, being sanded, or otherwise putting paint dust into the air you are fine - especially if that old paint has been covered with new. If the flooring is not showing contamination, then the walls are not shedding lead.