Dark Souls 2 was released for PS3 and Xbox 360 back in March 2014, ... Plus, as the statement above says, the PS4, PC, and Xbox One versions will still continue to function.

Dark Souls 2‘s PS3 and Xbox 360 servers are set to close on March 31, 2024, at 5am PT / 8am ET / 1pm GMT / 2pm CET. One More Soul Snuffed Out. ... Servers for PC, PS4, ...

“The Dark Souls 2 PS3 and Xbox 360 servers will shut down on March 31, 2024. ... PC, PS4 & Xbox One servers will not be affected. Thank you to those who have played since launch. ...

PS3 to PS4 is basically not done unless it was a PS3 exclusive game in the first place. The reason, as DisplayNameTaken alluded to, is the difference in the CPU (not so much the GPU) of the PS3.