The answer is "almost never". Qualifications below.
Learn the Cortex-M4 ecosystem first. You can do a remarkable amount of stuff by abusing microcontroller systems in weird ways. The tools for dealing with microcontrollers are MUCH better than the FPGA ecosystem tools (which suck--and that's on a good day).
If you need an FPGA, generally you know it. The first sign is: "There's no way to do this with my microcontroller." That step is generally followed by: "Is there a different microcontroller that could do this?" followed by asking the old greybeard "Is there really no way to do this on a microcontroller?" And finally, "Crud, this can't be done on a microcontroller"--at that point you can consider an FPGA.
As someone who has been dealing with this for mumble too many years, I've been slowly migrating functionality of my clients away from their FPGAs and into the microcontrollers more and more. It's just way easier on too many fronts--and they don't have to learn Verilog/VHDL. The FPGAs will never go away, but they will have the minimum functionality we can get away with.
> I've no experience with FPGA, but would like to learn.
I'm likely to get some static for this, but get an actual supported dev board and not an open-source hacker board. I would recommend something like this that has an academic version:
https://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=...
Use the manufacturer tools (which, in this instance, are free) as using an "open-source toolchain" is NOT for beginners.
Once you understand FPGA's a bit more thoroughly, then you can take the leap to the open source stuff.