fix(#2852): forward model overrides from categories/agent config to subagents

- fix(switcher): use lastIndexOf for multi-slash model IDs (e.g. aws/anthropic/claude-sonnet-4)
- fix(model-resolution): same lastIndexOf fix in doctor parseProviderModel
- fix(call-omo-agent): resolve model from agent config and forward to both
  background and sync executors via DelegatedModelConfig
- fix(subagent-resolver): inherit category model/variant when agent uses
  category reference without explicit model override
- test: add model override forwarding tests for call-omo-agent
- test: add multi-slash model ID test for switcher

src/create-managers.ts

@@ -9,6 +9,7 @@ import { initTaskToastManager } from "./features/task-toast-manager"
 import { TmuxSessionManager } from "./features/tmux-subagent"
 import { createConfigHandler } from "./plugin-handlers"
 import { log } from "./shared"
+import { markServerRunningInProcess } from "./shared/tmux/tmux-utils/server-health"
 
 export type Managers = {
   tmuxSessionManager: TmuxSessionManager
@@ -26,6 +27,7 @@ export function createManagers(args: {
 }): Managers {
   const { ctx, pluginConfig, tmuxConfig, modelCacheState, backgroundNotificationHookEnabled } = args
 
+  markServerRunningInProcess()
   const tmuxSessionManager = new TmuxSessionManager(ctx, tmuxConfig)
 
   const backgroundManager = new BackgroundManager(