Questions regarding PS4 on PS5 backwards compatibility – Beragampengetahuan

I am desperate. My PS4 was stolen. It had all my PS Store bought games installed on. I cannot simply buy a new console and download the games again because the licenses are tied to the console the titles are installed on. I am lead to understand that this is not issue on PS5, that I can simply log in to my PSN account and download my PS4 titles through backwards compatibility without further complications or any additional financial expense. Is this information correct? If yes, is PS Plus subscription required? I am not PS Plus user.

Thank you.