[BUG] Isolate parallel mode and provider profile writes

[easonLiangWorldedtech]

Problem

When multiple webview instances run in parallel mode, mode switches and provider profile changes are not properly isolated per view. This causes:

1. handleModeSwitch writes global state instead of per-view state
2. Provider profile divergence between parallel tabs — one tab changes the profile, others see stale data
3. Profile delete operations use merged (global) state instead of view-local state, causing incorrect deletions

Solution

Route all mode and provider profile write operations through the per-view state base introduced in PR #977:

• handleModeSwitch writes to view-local state instead of global state
• Provider profile upsert/activate/delete use merged view-local state for correct per-view behavior
• Profile divergence is resolved by each tab maintaining its own profile selection

Scope

• handleModeSwitch → view-local mode persistence
• Provider profile upsert, activate, delete → view-local-aware operations
• Depends on PR fix(webview): add durable per-view state base #977 (feat/view-local-state-base) for the per-view state foundation

Tests

• Targeted tests: 74 passed
• Expanded mode/API-related set: 200 passed
• Full core run: 2184 passed / 9 skipped

Related

• Old Issue [BUG] Multi-tab mode/model settings get overwritten by latest task #908 (historical context)
• Old PR fix(webview): isolate parallel provider view state #909 (parent PR)