I’m a fan of pavers. You’ll need 2” depth for the paver and remaining fill with limestone screenings to level the base.

Thank you!

Whatever type of product you choose, make the new “floor” as high as the other to avoid tripping.

I would absolutely extend the patio. Pavers would look nice or more cement

Add more pea gravel and get concrete pavers,

both relatively affordable and available at any home improvement store.

a good DIY project!

With that gorgeous view I would hang the swing so it is facing out. If the rest of the vista is as nice I would plan everything around that.

A couple pix of our paver patio. Enjoyed for 25+ years.

A paver extension is a great idea and can be a DIY project if you are up to it. My husband and I did a 12x12 patio ourselves (it was a lot of physical work) but used a grid system underneath to assure the pavers were evenly placed. Then filled with elastomeric sand that you water in between.

Paver to match the rest under the shed too.

We do pavers and gravel for the drainage and love the look. But you could simply do gravel, as @RedRyder point out, you want a seamless install. No tripping with the wine.

An underlayment will keep weeds at bay.