fix: add cmux __tmux-compat prefix to interactive_bash tool

Extract isCmuxCompatEnvironment to shared module and fix
interactive_bash to resolve cmux executables with the __tmux-compat
prefix, matching all other tmux command paths in the codebase.

src/shared/tmux/cmux-detect.ts

@@ -0,0 +1,11 @@
+/**
+ * Detect whether we are running inside cmux (cmux omo).
+ * When cmux-omo sets up the environment it injects a tmux shim and sets
+ * CMUX_SOCKET_PATH / TMUX. If detected, redirect tmux commands to
+ * `cmux __tmux-compat` so they become native cmux splits instead of
+ * failing because there is no real tmux server running.
+ */
+export function isCmuxCompatEnvironment(): boolean {
+	return Boolean(process.env.CMUX_SOCKET_PATH) ||
+		process.env.TMUX?.includes("cmuxterm") === true
+}

src/shared/tmux/index.ts

@@ -1,4 +1,5 @@
 export * from "./types"
 export * from "./constants"
+export * from "./cmux-detect"
 export * from "./runner"
 export * from "./tmux-utils"

src/shared/tmux/runner.ts

@@ -1,4 +1,5 @@
 import { spawn } from "../bun-spawn-shim"
+import { isCmuxCompatEnvironment } from "./cmux-detect"
 
 type RunTmuxOptions = {
 	retry?: number
@@ -29,18 +30,6 @@ function isTerminalTmuxError(stderr: string): boolean {
 	return TERMINAL_TMUX_ERROR_PATTERN.test(stderr)
 }
 
-/**
- * Detect whether we are running inside cmux (cmux omo).
- * When cmux-omo sets up the environment it injects a tmux shim and sets
- * CMUX_SOCKET_PATH / TMUX. If detected, redirect tmux commands to
- * `cmux __tmux-compat` so they become native cmux splits instead of
- * failing because there is no real tmux server running.
- */
-function isCmuxCompatEnvironment(): boolean {
-	return Boolean(process.env.CMUX_SOCKET_PATH) ||
-		process.env.TMUX?.includes("cmuxterm") === true
-}
-
 function resolveTmuxExecutable(tmuxPath: string): string[] {
 	if (!isCmuxCompatEnvironment()) {
 		return [tmuxPath]