Add private browser windows

Summary

Let users open private windows with a separate, ephemeral browsing context.

Scope

• Give private browsing its own Engine website-data partition, isolated from the regular profile.
• Keep private history, searches, favicons, session state, and blocker statistics in memory only.
• Remove ephemeral Engine data when the private context closes, including orderly shutdown cleanup.
• Show a clear private-window indicator and define whether private windows share one private context.
• Do not persist private browsing into the normal session restore.

Acceptance criteria

• Cookies and site storage cannot cross between regular and private browsing.
• Closing the private context leaves no browser-owned browsing records or Engine profile data behind.
• A crash or startup recovery does not restore private tabs.
• Existing PHOTON_TEMPORARY_PROFILE developer behavior remains useful for isolated runs.

Design reference: Zephium treats private browsing as an ephemeral profile kind: https://github.com/zephium-browser/Zephium/blob/main/crates/zephium-core/src/profiles.rs