Option to set minimum shutter speed in auto or shutter priority modes

I take many photos of my kids, and they are always moving. So I usually shoot in Shutter Priority at 1/250. Indoors it works fine because the ISO adjusts automatically, but in bright or outdoor light the images get overexposed. Then I have to quickly change the shutter speed or switch to Auto mode, and sometimes I miss the moment.

I would like a mode or option that lets me set a minimum shutter speed with Auto ISO for quick shots. Similar to the “Auto ISO with minimum shutter speed” feature available in Aperture Priority mode on mirrorless cameras.