Move stack context manager out of web

[dyladan]

As there is nothing web-specific about the stack context manager, and it may be useful in testing scenarios like #1344, we should consider moving the stack context manager out of web and into some place like core or into its own module.

[anpatellll]

I support this motion

[olamideTiana]

@dyladan May I take a look at this? I will suggest to refactor the code to separate the concerns of the web framework from the context management logic to identify what parts of the stack context manager depend on the web framework and developing a new context manager that handles the stack logic independently of the web framework.