Auto merge of #51656 - soc:topic/fix-home-dir, r=SimonSapin

Deprecate `std::env::home_dir` and fix incorrect documentation

Compare `std::env::home_dir`s claim:

> Returns the value of the 'HOME' environment variable if it is set and not equal to the empty string.

... with its actual behavior:

```
std::env::set_var("HOME", "");
println!("{:?}", std::env::var_os("HOME")); // Some("")
println!("{:?}", std::env::home_dir());     // Some("")
```

The implementation is incorrect in two cases:
- `$HOME` is set, but empty.
- An entry for the user exists in `/etc/passwd`, but it's `pw_dir` is empty.

In both cases Rust considers an empty string to be a valid home directory. This contradicts the documentation, and is wrong in general.

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