Add a button that lets you copy pre-formatted Markdown with Playground information

I used to use the "open a rust-lang/rust issue" link a lot to be able to quickly copy pre-formatted example code, a playground link, and stdout, but that feature was removed due to it being used for spam (#671).

It would be nice to have a replacement feature where it would let me copy what used to go into the GitHub issue body. E.g., it would output this to a textbox that could be copied:

Code ([playground](...)):

```rust
...
```

Output:

```
...
```

This would actually be even more useful to me than the old "open a rust-lang/rust issue" link because I often want to use the output in Zulip messages or issue or PR comments.

Originally posted by @camelid in https://github.com/integer32llc/rust-playground/issues/671#issuecomment-819171314

The issue names no files or tests. Start by locating the Playground interface that displays compiler output and the existing code, link, and stdout formatting; done means a button produces copyable Markdown containing the code, playground link, and output without reopening the GitHub issue flow.