refactor(web): source the search result bound from its protocol constant

`ConnectionHandle.sessionSearchResultLimit` mirrored
`SESSION_SEARCH_RESULT_LIMIT` as per-connection state, giving one fact two
homes in the same module and implying a transport-varying or server-negotiated
bound that the response schema's fixed `max` forbids. `SessionsService` now
reads the constant directly and its constructor drops the parameter; the
connection handle and its unreachable `/client` value re-export go away.

The import comes from the inline-safe wire layer rather than the connection
plugin's `/client` surface, which the bundle-purity gate rejects for value
imports.

packages/client/runtime/src/client/index.ts

@@ -113,11 +113,7 @@ export const inject = ['connection']
 export function apply(ctx: Context): void {
   ctx.plugin(SlotsService)
   const connection = ctx.get('connection') as ConnectionHandle
-  const sessions = new SessionsService(
-    ctx,
-    connection.api,
-    connection.sessionSearchResultLimit,
-  )
+  const sessions = new SessionsService(ctx, connection.api)
   const workspaces = new WorkspacesService(ctx, connection.api, sessions)
   ctx.effect(
     () => workspaces.startInitialSelection(),

packages/client/runtime/src/client/sessions/service.ts

@@ -19,6 +19,9 @@ import type { Context, Fiber } from 'cordis'
 import type {
   IApiClient, RpcError, RpcResult, SessionId, WorkspaceId,
 } from '@deepseek-ai/dsh-client-connection/client'
+// Value import from the inline-safe wire layer (not the connection plugin):
+// plugin-to-plugin value imports are a bundle purity error.
+import { SESSION_SEARCH_RESULT_LIMIT } from '@deepseek-ai/dsh-host-apiproxy/api'
 import type {
   HostObservable, SessionMaybeProvideInfo, SessionProvideInfo,
 } from '@deepseek-ai/dsh-client-ui-slots'
@@ -149,8 +152,13 @@ export interface SessionProvideDescriptor {
 
 /** Root sessions service: list store, current selection, object-layer manager, scope tree, bindings, ancestry. */
 export class SessionsService {
-  /** Fixed sidebar result bound supplied to presentation plugins as injected data. */
-  readonly searchResultLimit: number
+  /**
+   * The wire schema's own result bound, re-exposed for presentation plugins as
+   * injected data. Not per-connection state: the `session.search` response
+   * schema caps `items` at this constant, so every transport (fixture included)
+   * reports the same number.
+   */
+  readonly searchResultLimit = SESSION_SEARCH_RESULT_LIMIT
   /** List snapshot store (list RPC + host stream increments; re-pulled on reconnect) — the useSessions standard feed, current included. */
   readonly list: SnapshotStore<SessionListState>
   /** The object-layer instance cluster and frame dispatch entry. */
@@ -184,14 +192,11 @@ export class SessionsService {
   /**
    * @param ctx - client root context (scope fibers mount under it).
    * @param api - wire client shared with every Session.
-   * @param searchResultLimit - protocol-owned search bound from the connection service.
    */
   constructor(
     private readonly rootCtx: Context,
     api: IApiClient,
-    searchResultLimit: number,
   ) {
-    this.searchResultLimit = searchResultLimit
     this.selection = createSnapshotStore<{ sessionId?: SessionId }>(
       {},
       { persist: { name: 'dsh.sessions.current' } })