I have a Smart Tv that I have only used for Netflix so far, the exact name is
TCL U49P6006X1, 123 cm (49 inch), UHD 4K, SMART TV, LED TV, 1200 PPI, DVB-T2 HD, DVB-C, DVB-S, DVB-S2
We're a customer of Vodafone Kabel
Landline and Wi-Fi.
And my question is can I receive channels if I plug a cable into the multimedia socket or do I need a receiver / additional contract with Vodafone.
You can receive all unencrypted channels without a receiver directly on the TV, which if the TV connection costs additional costs. If that is not the case, you must also conclude a contract for a TV connection with Vodafone.
DVB-C says that the TV has a tuner for digital cable TV, if you want to see private TV in HD then you need a CI + module from Vodafone, and you have to book Basic TV Cable
https://zuhauseplus.vodafone.de/digital-fernsehen/kabel/basic-tv-cable.html