AI WS: Investigate Stagehand cashing

[nikitachapovskii-dev]

https://docs.stagehand.dev/v3/basics/extract#server-side-caching

see if we can implement this.

possible blockers:

• if we switch to env: BROWSERBASE, server-side caching becomes possible (typically enabled by default), but that requires infrastructure changes.
• Also, per-call cache control (serverCache: false/true) may not be available in our current version combo, even if baseline Browserbase caching works.