refactor(client): rename the provide reprojection to updateCurrentProvideInfo and privatize the id resolvers

provideInfo(id)/maybeProvideInfo(id) lost their last external caller
when the renderer host switched to the currentProvideInfo observable;
both become private (tests assert through the public projection). The
reprojection method's name now says what it does — re-derive and
publish on change — and matches the field family it maintains.

packages/client/runtime/tests/sessions-service.spec.ts

@@ -79,7 +79,8 @@ describe('scope tree', () => {
     expect(scopeOf(scoped as Context)).toBe('s1')
     expect(scopeOf(b.ctx)).toBeUndefined()
     const binding = b.svc.binding(sid('s1'))
-    expect(binding?.session).toBe(b.svc.provideInfo('s1')?.hooks['session'])
+    b.svc.open(sid('s1'))
+    expect(binding?.session).toBe(b.svc.currentProvideInfo.getSnapshot().hooks['session'])
     expect(b.svc.binding(sid('s1'))).toBe(binding)
     expect(binding?.ctx).toBe(scoped)
   })
@@ -183,16 +184,17 @@ describe('current selection (migrated from ui-layout, arbitrated into the list s
 })
 
 describe('cell (render-layer session kit)', () => {
-  it('resolves an identity-stable {sessionId, session} cell; unknown ids yield undefined', async () => {
+  it('resolves an identity-stable {sessionId, session} cell through the current projection', async () => {
     const b = bench()
     await feedList(b, [{ id: 's1' }])
-    const info = b.svc.provideInfo('s1')
-    expect(info).toBeDefined()
-    expect(info?.sessionId).toBe('s1')
+    b.svc.open(sid('s1'))
+    const info = b.svc.currentProvideInfo.getSnapshot()
+    expect(info.sessionId).toBe('s1')
     // The bundle carries bare observables; hook binding happens in React.
-    expect(info?.hooks['session']).toBe(b.svc.binding(sid('s1'))?.session)
-    expect(b.svc.provideInfo('s1')).toBe(info)
-    expect(b.svc.provideInfo('ghost')).toBeUndefined()
+    expect(info.hooks['session']).toBe(b.svc.binding(sid('s1'))?.session)
+    // Re-staging the same id republishes nothing: identity holds.
+    b.svc.open(sid('s1'))
+    expect(b.svc.currentProvideInfo.getSnapshot()).toBe(info)
   })
 
   it('currentProvideInfo follows selection: absent projection ↔ definite bundle, notified on each move', async () => {
@@ -204,10 +206,14 @@ describe('cell (render-layer session kit)', () => {
     const notified = vi.fn()
     b.svc.currentProvideInfo.subscribe(notified)
     b.svc.open(sid('s1'))
-    expect(b.svc.currentProvideInfo.getSnapshot()).toBe(b.svc.provideInfo('s1'))
+    const s1Bundle = b.svc.currentProvideInfo.getSnapshot()
+    expect(s1Bundle.sessionId).toBe('s1')
+    expect(s1Bundle.hooks['session']).toBe(b.svc.binding(sid('s1'))?.session)
     expect(notified).toHaveBeenCalledTimes(1)
     b.svc.open(sid('s2'))
-    expect(b.svc.currentProvideInfo.getSnapshot()).toBe(b.svc.provideInfo('s2'))
+    const s2Bundle = b.svc.currentProvideInfo.getSnapshot()
+    expect(s2Bundle.sessionId).toBe('s2')
+    expect(s2Bundle).not.toBe(s1Bundle)
     expect(notified).toHaveBeenCalledTimes(2)
     b.svc.clear()
     await Promise.resolve() // clearSelection projects through the manager notifier
@@ -249,12 +255,11 @@ describe('cell (render-layer session kit)', () => {
     expect(notified).not.toHaveBeenCalled()
   })
 
-  it('provideInfo()/binding() are pure resolution: no staging, no deferred sweep', async () => {
+  it('binding() is pure resolution: no staging, no deferred sweep', async () => {
     const b = bench()
     await feedList(b, [{ id: 's1' }, { id: 's2' }])
     b.svc.open(sid('s1')) // staged
-    b.svc.provideInfo('s2') // resolution only — must NOT move the stage
-    b.svc.binding(sid('s2'))
+    b.svc.binding(sid('s2')) // resolution only — must NOT move the stage
     await feedList(b, [{ id: 's2' }]) // s1 removed: still staged → deferred, scope survives
     expect(b.svc.scope(sid('s1'))).toBeDefined()
   })
@@ -265,7 +270,6 @@ describe('cell (render-layer session kit)', () => {
     const historyCalls = () => b.api.calls.filter(c => c.method === 'session.history')
     // Resolution is addressing, not staging: no window pull.
     b.svc.scope(sid('s1'))
-    b.svc.provideInfo('s1')
     b.svc.binding(sid('s1'))
     expect(historyCalls()).toHaveLength(0)
     b.svc.open(sid('s1'))