Serialize outputs in separate file so app can be viewable when auto-instantiate is off

[mscolnick]

Description

Serialize outputs in separate file so app can be viewable when autorun is off. This is different from persistent caching, even if configured on all cells. This is much cheaper and just stores the HTML of the outputs (which can be easily found in the SessionView), this does not "hydrate" the runtime, so all outputs will be considered stale.

This helps with users who always use auto-instantiate=off

Suggested solution

SessionView has a serialize/deserialize function on it that can read/write to an outputs file. This will be stored in the shared __marimo__ folder, similar to persistent cache and auto-export.

Proposed path would be __marimo__/outputs.json.
Other options could be __marimo__/session.json, if somehow it ends up containing more than outputs (variables, datasets schemas, etc)

Alternative

No response

Additional context

No response