Do I need to replace my chain?
You need a chain wear gauge or other accurate chain wear/length measurement to be sure. Chains shouldn’t be used past 0.75% elongation. For modern 11 or 12 speed chains I’ve even heard 0.5%.
A worn chain will accelerate cassette wear, especially if the cassette is new.
On new chainrings a worn cassette can cause chain suck.
50km per week over 4 months is 800km. That’s usually not enough to reach 0.5% elongation unless you were riding in adverse conditions (e.g. mud, sand, dust, rain) with high power and/or didn’t clean and lube the chain.
If your current chain is only somewhat worn you could get a new one for the new cassette but keep the used chain for later. After the cassette has been through one or two chains you can use the used chain.