Tables that have not changed between re-renders flicker

[mofojed]

When you update the state of a component, tables that should not be affected by the change "flicker".

You can see this problem manifest following these steps:
Steps to Reproduce:

1. Create a widget with a table that remains the same across re-renders and another table that changes across re-renders, e.g.:

import deephaven.ui as ui
from deephaven.plot.express import data

stocks = data.stocks()

@ui.component
def my_widget(source):
    value, set_value = ui.use_state("CAT")

    return [
        ui.panel(ui.text_field(value=value, on_change=set_value, label="sym"), title="Sym Input"),
        ui.panel(source, title="Source"),
        ui.panel(source.where(f"sym=`{value}`"), title="Filtered")
    ]

mw2 = my_widget(stocks)

2. Make changes in the text-field to update the Filtered table

Expected Results
2. Only the Filtered table should blink/update

Actual Results
2. The table that is not being changed flickers when changes are made

Right now with every change, we are re-sending the full document (#123) and re-sending all exported objects. This causes tables that have not been changed to flicker. We do not need to send items we have already sent.