Hi, Jan.
Like you, I have a 2010 Mac Pro. I've been upgrading it and the performance, for a 10 year old computer, still impresses me.
We have two iMacs in the house, but I wouldn't use them for photo editing because I'm sensitive to the glossy screen; would seriously miss the ability to rotate the screen 90 degrees for profile shots; and have a strong preference for my NEC color calibrated monitor.
Should you keep your classic Mac Pro, you might want to consider an OWC PCIe 6G SSD for the operating system (480GB for $169) and a second PCIe 6G SSD for your Photoshop scratch disk. I'm using a WD 2TB 6G Blue drive ($230 at Newegg) mounted on an OWC Accelsior S PCIe Adapter ($42.75). These drives will be fast and you can leave your data and time machine on inexpensive hard drives in the four upper expansion bays.
As you mentioned, a new video card is a must to upgrade to Mojave. You can get an Apple recommended Radeon RX 580 8GB for $299 at OWC. That's what I'm using, and the upgrade to Mojave was a snap. It has display port, HDMI and DVI-D connectivity.
So, for $740.75, plus tax, you have a fast and very capable Mojave machine that will perform well while you wait for the next big thing. That's what I'm doing, anyway.
One item you didn't mention is memory. The funny thing about Photoshop is that it isn't yet optimized to take advantage of my 10 year old six core Westmere Xeon processor, nor my 8GB Radeon GPU. What it does crave is memory. Earlier today I focus-stacked 30 raw files from a Nikon D850. It was slow going, but when I checked the activity monitor, the problem wasn't the CPU. It wasn't stressed at all. It was Photoshop consuming almost all of my 48GB of memory.
Whatever route you take, try to get as much memory as possible. The new Mac Mini looks very interesting, but I noticed that it tops out at 64GB of memory. For me, when it's time to put my Mac Pro in the museum I'll want at least 96GB of memory, with the opportunity to add more in the future.
Good luck!
Best,
Jeff