The iPad Pro cannot run OS X apps. What you already know about using iPad as a desktop substitute (in your particular circumstances) carries over to the iPad Pro, for the most part. Other than raw processing power, the main differences between that and other iPads (for productivity) are Slide-over and Split View multitasking (available on other new iPad models as well), the display (size as well as quality), Pencil, and Smart Keyboard.
I don't think you'll find full iOS substitutes for all the apps you list, although you may, depending on how you use Photoshop, Lightroom, and Filemaker (there are iOS versions of all of those). There are no "iPad Pro-only" apps (though some will have extra support/capabilities for Pencil) - just shop App Store on your iPad 4 and see what's out there.
Have you considered using the iPad for remote-control of your primary computer as a possible way around all this? Even so, controlling OS X apps with an iPad may be sub-optimal.
I have the Pro, and am quite happy, but for my purposes, I was able to use the first-generation iPad as a laptop substitute. Slide-over and Split View have provided big improvements to the way I work (researching and writing simultaneously, for example), as has better support for keyboard shortcuts. The amount of photo editing I need to do in the field (quick work prior to uploading for web publishing) is supported, but I don't try to do the kind of intensive editing that can be accomplished in the full version of Photoshop.
If you want to work locally with the full apps you're used to, a new MacBook Pro is probably the way to go. While you could (as suggested) replace the spinning HDD with an SSD and max-out the RAM (if you haven't already done so)... your current MacBook probably won't have many more years of useful life, regardless. It won't upgrade beyond El Capitan. While not a problem currently, since you're also running El Cap on your Mac Pro, other software upgrades may require you to go beyond El Capitan on both machines. Also, you may appreciate having a Retina display.
As to the whole "it doesn't have Finder" thing.... iOS doesn't have Finder-like capabilities for local storage, but if you're working on the same project on multiple machines, local storage may not be the right approach. iCloud Drive, Google Drive, DropBox... all have familiar, folder-based interfaces. (As someone who got accustomed to using corporate file servers decades ago, local storage is way more than "yesterday.")