Replace async-watch with a custom watch (#32245)

The `async-watch` crate doesn't seem to be maintained and we noticed
several panics coming from it, such as:

```
[bug] failed to observe change after notificaton.
zed::reliability::init_panic_hook::{{closure}}::hea8cdcb6299fad6b+154543526
std::panicking::rust_panic_with_hook::h33b18b24045abff4+127578547
std::panicking::begin_panic_handler::{{closure}}::hf8313cc2fd0126bc+127577770
std::sys::backtrace::__rust_end_short_backtrace::h57fe07c8aea5c98a+127571385
__rustc[95feac21a9532783]::rust_begin_unwind+127576909
core::panicking::panic_fmt::hd54fb667be51beea+9433328
core::option::expect_failed::h8456634a3dada3e4+9433291
assistant_tools::edit_agent::EditAgent::apply_edit_chunks::{{closure}}::habe2e1a32b267fd4+26921553
gpui::app::async_context::AsyncApp::spawn::{{closure}}::h12f5f25757f572ea+25923441
async_task::raw::RawTask<F,T,S,M>::run::h3cca0d402690ccba+25186815
<gpui::platform::linux::x11::client::X11Client as gpui::platform::linux::platform::LinuxClient>::run::h26264aefbcfbc14b+73961666
gpui::platform::linux::platform::<impl gpui::platform::Platform for P>::run::hb12dcd4abad715b5+73562509
gpui::app::Application::run::h0f936a5f855a3f9f+150676820
zed::main::ha17f9a25fe257d35+154788471
std::sys::backtrace::__rust_begin_short_backtrace::h1edd02429370b2bd+154624579
std::rt::lang_start::{{closure}}::h3d2e300f10059b0a+154264777
std::rt::lang_start_internal::h418648f91f5be3a1+127502049
main+154806636
__libc_start_main+46051972301573
_start+12358494
```

I didn't find an executor-agnostic watch crate that was well maintained
(we already tried postage and async-watch), so decided to implement it
our own version.

Release Notes:

- Fixed a panic that could sometimes occur when the agent performed
edits.

crates/remote_server/Cargo.toml

@@ -24,7 +24,6 @@ test-support = ["fs/test-support"]
 [dependencies]
 anyhow.workspace = true
 askpass.workspace = true
-async-watch.workspace = true
 backtrace = "0.3"
 chrono.workspace = true
 clap.workspace = true
@@ -63,6 +62,7 @@ smol.workspace = true
 sysinfo.workspace = true
 telemetry_events.workspace = true
 util.workspace = true
+watch.workspace = true
 worktree.workspace = true
 
 [target.'cfg(not(windows))'.dependencies]