[release/10.0] [Blazor][HotReload] Capture the execution context before calling RenderRootComponentsOnHotReload

[github-actions]

Backport of #63846 to release/10.0

/cc @javiercn

[Blazor][HotReload] Capture the execution context before calling RenderRootComponentsOnHotReload

Ensure ExecutionContext flows to hot reload re-renders

Description

• capture the current ExecutionContext when subscribing to HotReloadManager.OnDeltaApplied
• invoke RenderRootComponentsOnHotReload via a helper that restores the captured context, preserving AsyncLocal values
• add a regression test that simulates hot reload and confirms AsyncLocal data survives the re-render

Fixes #45741

Customer Impact

AsyncLocal-backed data (e.g., culture, logging scopes, circuit state) was being lost after hot reload, leading to incorrect behavior on subsequent renders.

Regression?

• Yes
• No

Risk

• High
• Medium
• Low

Changes are scoped to the hot reload subscription path, reuse existing render logic, and are exercised by automated tests.

Verification

• Manual (required)
• Automated

Packaging changes reviewed?

• Yes
• No
• N/A

[javiercn]

With video verification
https://github.com/user-attachments/assets/acdebbc2-1617-491e-9bc2-24df281fdb6d

[wtgodbe]

@javiercn has this one gone thru ask-mode yet?