BUG: Styler export() and use() no longer work after Styler has been rendered.
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.

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Addressing #39396 and #39395 means that after `Styler._compute()` or `Styler.render()` the `_todo` list is cleared.

Since `Styler.export = lambda x: Styler._todo`
and `Styler.use = lambda x: Styler._todo.extend(x)`

This means that exporting `styles` cannot be achieved if a Styler has been rendered at least once.

Possible actions:

1) Update the docs to make users aware of the new behaviour and suffer any regression issues for `export` `use`.
2) Revert the original PR, suffering the duplicate CSS in HTML generated on each render.
3) Solve both issues by clearing the `.ctx` object before render and keeping the `_todo` list, suffering the need to recompute all applied styles on each render.

Perhaps 3 is best - If performance is an issue developers should know only to every render once?
