Unwrap NestedServletException in codegen

[IlyaMuravjov]

Description

Fixes #2586

How to test

Manual tests

Expected behavior from #2586 should be observed for versions of Spring before and after 6.0.

Self-check list

• I've set the proper labels for my PR (at least, for category and component).
• PR title and description are clear and intelligible.
• I've added enough comments to my code, particularly in hard-to-understand areas.
• The functionality I've repaired, changed or added is covered with automated tests.
• Manual tests have been provided optionally.
• The documentation for the functionality I've been working on is up-to-date.