Expose the context init script just a teeny tiny bit pretty please 😻

[eastlondoner]

1. So @pkiv doesn't end up making PRs on a Sunday like this:
   Bundle the Stagehand DOM script for better portability eastlondoner/cursor-tools#20
2. It's needed if someone wants to set up their own playwright contexts
3. It needs to be used in a slightly different way to bootstrap to an already running CDP server

But mainly reason 1, Paul's a great guy I'm sure he has better things to do on a Sunday.

A private static field on a class would be fine really, just some way for code that depends on Stagehand to access it. Right now it's closured in to functions in a way that makes it inaccessible, at least as far as I can tell.

[kamath]

thanks for the issue and the feedback!!

encourage the audience here to check out the wonderful work done on cursor-tools and this phenomenal stagehand integration