Beretta 1301 or A300 can be adjusted by removing the butt plate and adding/removing included spacers using a screwdriver. If you install an adapter to use the Magpul shotgun stock it's even easier. Will look and feel like a ye-olde shotgun but be extremely light. Be careful though as full power loads will hurt.

A second-hand (pre-Cerberus/Freedom Group) Remington 1100 or 11-87 in twenty-gauge. I am partial to the “special field” version with the straight grip.

Any adjustable LOP would be aftermarket, or you can have her measured and get the factory stock altered by a competent gunsmith. Note that I wrote “gunsmith,” not “AR assembler” - the two are conflated far too often these days.

In several places it's illegal to have a semi-auto shotgun with both a pistol grip and a collapsible stock. It's also illegal to have a shotgun under 26 inches in length or a shotgun barrel under 18 inches.

The Benelli Ultralight at 6.1 lbs is probably your best option. Here's an article with a few more options.

https://www.fieldandstream.com/guns/lightweight-12-gauge-shotguns/

Is semi-auto a hard requirement? Asking because I have long preferred break action at the range, and most trap/skeet shooters I've seen prefer pump or break actions.

If you're open to break action, something like the Stoeger Condor Compact in 20-gauge could be a good fit for a smaller adult:
https://stoegerindustries.com/shotguns/condor-compact-shotguns?eid=253

You could also consider a 20 gauge shotgun. They tend to be much smaller and certainly have less recoil.

Does the stock length of pull need to convert back and forth? Is she small enough for a youth model?