Depending on the publication type, Open Access publication charges (= APC Article Processing Charges) are treated differently:
APCs in pure OA journals may be subsidized.
Depending on the existing contract with the publisher, OA publishing in hybrid journals is included, discounted, or must be paid for in full. Fees of transformation contracts are centrally financed and/or, if applicable, allocated on a flat-rate basis (analogous to existing subscription contracts): no costs are incurred for the individual authors.
Regardless, there are publishers who will bill you individually per item. Others bill the APCs via a central collective invoice to the university library. The latter is a formal step that does not allow any conclusions regarding central cost absorption. If applicable, the UB will continue to bill in full (plus the applicable 19% tax) after publication. On the other hand, you will find contract offers on the publishers' homepages that the UB has not joined.
Further notes.
All this information refers only to the OA publication costs - color and page charges, review fees, overlength fees, etc. are additional services and will be billed directly to you in addition, if applicable.