How does a size L Shaver Lake jacket fit?

The listed measurements are 22 inches armpit to armpit, 17 inches armpit to cuff and 24 inches collar to hem. That is a short, waist-length body with near-full-length sleeves. Check those figures against a jacket you already own.

Is this jacket rigid or stretch denim?

It is described as denim with no stretch mentioned. Expect a firmer feel that softens with wear rather than a stretchy fit.

What can I layer under it?

The 22-inch chest leaves room for a t-shirt or a light knit. Bulkier hoodies will likely feel tight across the shoulders.

Will the sleeves be long enough?

The 17-inch armpit-to-cuff measurement puts the cuff close to the wrist on average arms. On shorter arms the sleeves may need rolling.

Is it a good pick over a stretch-denim jacket?

If you want a jacket that keeps its shape and looks sharper over time, rigid denim is the better choice. If you want instant comfort and give, a stretch version suits better.