On the ps4 I have very unstable internet when I play with WLAN, with lan cable it is more stable but we have moved and that is not possible now. If I install a devolo dlan network and connect a LAN cable to the dlan part and then connect it to the ps4, is it as if I would connect my ps4 directly to the router via LAN cable?
It is difficult to predict. It depends on how the cables are installed in your house and whether there are any devices that cause interference. DLan works very well for some and very poorly or not at all for others.
So I have no choice but to test it.
Exactly.
I assume that it should be better than if you were using Wi-Fi. However, I doubt that you will get exactly the same ping as with a directly connected LAN cable. Of course, there remains the risk that your power lines in the house are so bad that it works very badly. You never have 100% security. But I would say that it will definitely be worth it.