[JS][J3] Separate Node and browser adapters and validate SSR/hydration

[code-tc]

Objective

Implement explicit Node and browser adapters behind the same JS-client contract, preserving user delegation in Node and preventing privileged code or credentials from entering browser bundles, HTML or hydration state.

Acceptance criteria

• Conditional exports/build checks prove browser bundles exclude Node credential/storage modules.
• SSR and browser hydration use the same public client contract.
• User-delegated and service-owned Node operations are explicit and auditable.
• Session expiry, revocation, cross-tenant, hostile hydration and confused-deputy tests fail closed.
• Playwright verifies the full SSR → hydration → authenticated request flow.

Parent: #74

Tembo execution contract

automation:
  eligible: true
  executor_profile: tembo
  readiness: blocked
  primary_repository: TinyChain-Inc/client
  base_branch: main
  writable_scope:
    - js/src/**
    - js/tests/**
    - web/src/**
    - web/tests/**
    - web/scripts/**
    - web/package.json
    - web/package-lock.json
  prerequisites:
    - "#85"
    - "TinyChain-Inc/tcv2#51"
    - "TinyChain-Inc/tcv2#53"
  concurrency_group: js-runtime-adapters
  required_commands:
    - "cd web && npm ci"
    - "cd web && npm run test:all"
  external_actions: none
  draft_pr_only: true
  completion_authority: human
  visual_validation:
    required: false
    evidence: []
  budget:
    size: large
    max_revisions: 3
    max_wall_minutes: 120