Yes, you can link both versions to the same account, and then play the same character from either platform. It requires (as you already mentioned) buying the game twice, once getting the PS4 version and once getting the PC version. (You get 30 days of game time included with each of those purchases, so the second one saves you a month's worth of subscription fees, offsetting at least part of the extra cost.)

There are some issues regarding data that's stored locally. Your UI layout, hotbars, macros, and gear sets are stored on your local machine, so each time you switch back and forth you'll have to re-do any changes to those that you made on the other platform if you want them to keep working the same. (The UI you may want different between your PC monitor and your TV anyway, and in any case, most people don't change it that often. And if you're playing from keyboard on PC and controller on PS4, you'd have different hotbars anyway. But the gear sets and macros can be annoying to keep up to date on multiple platforms.)