Izby uznawane były za związki publicznoprawne, działające poprzez własne organy i posiadające jasno określone kompetencje.
The chambers were considered as public associations, operating through their own bodies and having clearly defined abilities.
https://bsawp.edu.pl/wp-content/uploads/2020/08/Kliczek-Pasn...


Public association means any association, organization, or society whose members include elected or appointed public officials and for which public funds are used or paid to the public association for membership dues or for other support for the official's participation in the public association.

https://www.lawinsider.com/dictionary/public-association

This is a tough one, as it may be understood in the sense of a 'political entity' in the sense of polis, res publicae, etc., i.e., a national or local government. In the above context, it seems that it may also refer to other special-purpose entities (such as a port authority, special economic zones, environmental protection areas, etc.) with statutory/legal force, rather than a 'government' in itself.

I would suggest the following full translation in this context:

Special government entities include statutory bodies of a compulsory nature, whose competences comprise a strictly defined sphere of activity (professional, economic, cultural, religious, national).

Depending on the broader context, 'samorząd [specjalny]' may also be '[special] self-governments', though this translation is overused and often excessively literal.