Proxy path fixes (#4548)

* Fix issue where HTTP error status codes are not read.

* Fix issues surrounding sessions when accessed from a proxy.

- Updated vscode args to match latest upstream.
- Fixed issues surrounding trailing slashes affecting base paths.
- Updated cookie names to better match upstream's usage, debuggability.

* Bump vendor.

* Update tests.

* Fix issue where tests lack cookie key.

Co-authored-by: Asher <ash@coder.com>