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/shared/tmux/tmux-utils/server-health.ts

@@ -1,11 +1,20 @@
 let serverAvailable: boolean | null = null
 let serverCheckUrl: string | null = null
+let inProcessServerRunning = false
 
 function delay(milliseconds: number): Promise<void> {
 	return new Promise((resolve) => setTimeout(resolve, milliseconds))
 }
 
+export function markServerRunningInProcess(): void {
+	inProcessServerRunning = true
+}
+
 export async function isServerRunning(serverUrl: string): Promise<boolean> {
+	if (inProcessServerRunning) {
+		return true
+	}
+
 	if (serverCheckUrl === serverUrl && serverAvailable === true) {
 		return true
 	}