Scene developer SocraticBliss has published an implementation of the PS4 7.02 Kernel Exploit, combined with Sleirsgoevy’s port of the recent webkit exploit. In parallel, Sleirsgoevy has been working on his own integration of the Jailbreak + Mira support, but reports that homebrew does not work at the moment.
To rephrase: if you own a PS4 running on firmware 7.02, there are now exploit releases floating around that give you kernel access, but not what people would consider a usable jailbreak yet. Once again, it is probably only a matter of days, if not hours, before a jailbreak usable by most people gets released.
One important caveat here is that the webkit exploit itself (the entry point to gaining control of the console) has a low success rate (reported to be 10% so far), which means that launching the exploit involves a lot of “reloading the page” on the PS4 browser (some people reported getting it to work after no less than 30 retries), at least for now. This could improve if people look at ways to improve the reliability of the webkit exploit.
I wouldn’t call the current releases “usable” for the end user, but people with the right set of skills might want to give a look, to either SocraticBliss’s User+Kernel implementation, Or Sleirsgoevy User+Kernel+Mira.

PS4 7.02 full stack exploit (user + kernel) released, Mira and Homebrew support in progress -