Xcode: Any way to refresh/re-run the playground?

Try Editor > Execute Playground from Xcode menu

I don't know what Reset Playground is, by the way.

In addition to the other responses, playground execution can also be controlled with the button on the bottom bar above the debugger console. There are two buttons on the left side of the console; the one on the left opens/closes the console and the one on the right controls the execution of the playground and changes depending on whether the playground is currently running.

If you hover over the button a small black triangle will appear in the bottom corner of the button. If you long press on the button the menu in the screenshot below will appear, where you can change the execution mode of the playground between automatically or manually running. If it's automatic, then it should run once every time you make a change (unless you make a change while it's running, then it will interrupt itself and run again). If it's manual then you have to press the button to run the playground.

While running the button is a hollow square, like a stop button on a VCR. Pressing it will stop the execution.

When it's not running it is a blue triangle, like a play button on a VCR. Pressing it will run the playground.

(Running Xcode 8.3)

Also, you can create your shortcuts.

Xcode > Preferences > Key Binding > (Search Execute Playground)

It is empty as a default, but you can assign anything.

Xcode 11 > Preferences > Key Binding > (Run Playground)