file_server: Chrome DevTools Workspaces stopped working

**Describe the bug**

The [Chrome DevTools Workspaces](https://developer.chrome.com/docs/devtools/workspaces/) feature, which allows editing local source files directly from the inspector (💕), stopped working in combination with a local `file_server`. I bisected the problem, and it appeared between `v0.102.0` and `v0.103.0`, which [leads](https://github.com/denoland/deno_std/compare/0.102.0...0.103.0) to https://github.com/denoland/deno_std/pull/1028.

Indeed, [this SO answer](https://stackoverflow.com/a/48440544/2079386) suggests that the Workspaces feature looks at the date headers in the response, and those were added in #1028.

**Steps to Reproduce**

Serve a basic static site with `file_server`, visit the site in chrome and follow [these steps](https://developer.chrome.com/docs/devtools/workspaces/#devtools) to set up Workspaces.

**Environment**

[Here is a screenshot](https://user-images.githubusercontent.com/6933510/169329965-48014ce1-4d3a-435b-897c-e09435441769.png) of the headers of a (recently edited) file, next to my local time, which is GMT+2. It looks correct.

- OS: MacOS 12
- deno version: 1.19.2
- std version: Working on v0.87.0 until v0.102.0, broken on v0.103.0 until v0.140.0.