I received a decision on granting a temporary residence permit for a foreigner's family member until 16/02/2023, but the card has not yet been printed. Can I take up employment if the card itself has not yet been collected?

The right to take up employment results from the type of permit granted. If you received a temporary residence permit for a foreigner's family member, e.g. granted under the art. 159 of the Foreigners' Act, you can take up employment even if you have not yet received your residence card. 
The entitlement results from the legal basis of your decision. A residence card is a document issued following the decision and allowing, among others to cross the borders repeatedly.
On our website in the section: Procedures/Employment of a foreigner/Work permit/Check if you need a work permit for your employee - you will find all categories of temporary residence permits that entitle you to take up employment: https://migrant.poznan.uw.gov.pl/en/procedury/work-permit.
Information about your right to take up employment should also be included in the instruction of your decision. If you still have doubts, feel free to contact us and ask about it.