use the platform's binary resolver instead of a second copy

teaBinary hardcoded ~/.local/bin:$PATH. Right for tea, wrong as a habit: iris wrote the same function
with ~/.cargo/bin added, the two disagreed, and a rustup-only machine was refused a plugin its own
sidecar could build.

locateBinary asks the owner's login shell, so it knows about every directory a per-user installer
added without anyone listing them. Verified it still resolves tea from ~/.local/bin, which is the case
the comment above it was written for.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

sidecar/tea-config.ts

@@ -3,6 +3,7 @@ import { homedir } from 'node:os';
 import { join } from 'node:path';
 import { getUserById } from 'officerdb';
 import { osUserHome, runAs } from '@@/os-user';
+import { locateBinary } from '@@/plugins/os-deps';
 
 // Reading and writing `tea`'s own config, per user.
 //
@@ -45,9 +46,14 @@ const isOwnerUser = (osUser: string | null): boolean => !osUser || osUser === pr
  *
  * Resolved once per call rather than cached: an install can add it while this process is running, and a
  * cached "missing" would outlive the thing that fixed it.
+ *
+ * `locateBinary` is the PLATFORM's resolver, not a copy of it. This used to hardcode
+ * `~/.local/bin:$PATH`, which was right for tea and wrong as a habit — iris wrote the same function with
+ * `~/.cargo/bin` added, the two disagreed, and a rustup-only machine was refused a plugin it could build.
+ * The shared one asks the owner's login shell, so it knows about every directory a per-user installer
+ * added without anybody listing them.
  */
-const teaBinary = (): string =>
+const teaBinary = (): string => locateBinary('tea') ?? 'tea';
-  Bun.which('tea', { PATH: `${join(homedir(), '.local', 'bin')}:${process.env.PATH ?? ''}` }) ?? 'tea';
 
 const configPathFor = (home: string): string => join(home, '.config', 'tea', 'config.yml');