Batter runner/ 1st baseman contact

[Little Jimmy]

Utrip tourney but any rule set is good. My question is about a play that didn't happen, but I wondered what would have been the ruling if a different scenario took place. This is what did happen...

Batter hits a hard spinner about half way up the first base line in foul territory. It spins hard as F3 runs down the line. As BR is approaches, F3 touches ball in foul territory. Nothing but a foul ball.

But what if F3 picked up the ball in fair territory in this scenario and instead of simply waiting to put a tag on BR, she turns and attempts to beat the BR to 1st base. And as BR attempts to outrun F3, there is contact of the feet, with F3 falling and BR reaching 1st safely?

Do you have basic interference? Did she "illegally" impede F3? Doesn't the BR have a right to attempt to beat F3 in a footrace to the bag? Am I overthinking everything?