plugins: exclude runtimeSubagentMode from loader cache key

The plugin loader cache key included runtimeSubagentMode, which is
derived from allowGatewaySubagentBinding. Since different call sites in
the message processing pipeline pass different values for this flag,
each call produced a distinct cache key, triggering redundant
register() calls (40+ in 24 seconds after startup).

runtimeSubagentMode does not affect which plugins are loaded or how
they are configured — it is only metadata stored alongside the active
registry state. Removing it from the cache key lets all call sites
share the same cached registry regardless of their binding mode.

Fixes #61756

src/plugins/loader.ts

@@ -285,7 +285,6 @@ function buildCacheKey(params: {
   includeSetupOnlyChannelPlugins?: boolean;
   preferSetupRuntimeForChannelPlugins?: boolean;
   loadModules?: boolean;
-  runtimeSubagentMode?: "default" | "explicit" | "gateway-bindable";
   pluginSdkResolution?: PluginSdkResolutionPreference;
   coreGatewayMethodNames?: string[];
 }): string {
@@ -321,7 +320,7 @@ function buildCacheKey(params: {
     installs,
     loadPaths,
     activationMetadataKey: params.activationMetadataKey ?? "",
-  })}::${scopeKey}::${setupOnlyKey}::${startupChannelMode}::${moduleLoadMode}::${params.runtimeSubagentMode ?? "default"}::${params.pluginSdkResolution ?? "auto"}::${gatewayMethodsKey}`;
+  })}::${scopeKey}::${setupOnlyKey}::${startupChannelMode}::${moduleLoadMode}::${params.pluginSdkResolution ?? "auto"}::${gatewayMethodsKey}`;
 }
 
 function normalizeScopedPluginIds(ids?: string[]): string[] | undefined {
@@ -434,7 +433,6 @@ function resolvePluginLoadCacheContext(options: PluginLoadOptions = {}) {
     includeSetupOnlyChannelPlugins,
     preferSetupRuntimeForChannelPlugins,
     loadModules: options.loadModules,
-    runtimeSubagentMode: resolveRuntimeSubagentMode(options.runtimeOptions),
     pluginSdkResolution: options.pluginSdkResolution,
     coreGatewayMethodNames,
   });