OK, I solved it. The following does work:

$agent->follow_meta_redirect;
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but only if you do NOT also have this in your code:

$agent->requests_redirectable( [] );
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Alternately, you can also just parse the content returned by:

$post_response->decoded_content()
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when the page containing the redirect is first loaded, and get the redirect URL from that. Again, the key is that you must NOT have:

$agent->requests_redirectable( [] );
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in your code. I think it's strange that if you enable redirects you still must manually retrieve the redirect URL, and if you disable redirects then even manually retrieving the URL doesn't work.