I think there might be a misconception around what an FPGA actually is and when it is used in designs. So let me try to explain that part first.
FPGAs and when one might want to have one...
At risk of simplication, an FPGA is little more than a processor that happens to be 'reconfigurable'.
Why would someone want a 'reconfigurable' microprocessor? Well, because it costs far too much to fabricate a silicon processor to afford to do it for one, two, or even two hundred chips. You'd need to be running batches of thousands of chips to make it economically feasible.
Since no design is ever bug-free the first time round, going the silicon route effectively commits a company to at least two if not more test runs, all at huge fabrication costs.
Which essentially means that very few commercial companies are going to be interested in designing and bringing to fabrication anything other than chip with broad enough commercial appeal.
So, if you come up with a brilliant design that justifies a custom microprocessor, then you might try to bring your idea to life on a shoestring budget by implementing it in an FPGA, where the actual chip is simply a collection of gates, and a 'program' (typically VHDL or Verilog) arranges those gates into an actual microprocessor.
But that's quite a ways down an entirely different (microprocessor design!) road...
Which leads me to suggest that
... FPGAs are not essential to robotics -- at least at the outset
What you need for robotics is a processor. An FPGA is just a special kind of processor (reconfigurable).
You ask whether you 'should'? Well that depends on your knowledge as well as where your real interests lie -- microprocessor design first or robotics first?
If microprocessors are your passion, then by all means! And robotics is a great application area for custom microprocessors -- perhaps a vision cortex with many parallel decision pathways handled directly in hardware, or special tensor multiplication in hardware -- basically anything that generic processors can't handle well off-the-shelf.
But if you're going to microprocessor designs in FPGAs, well, then of course you'll need to have all of that low level knowledge you mention, and more -- because fundamentally you'll be designing your own processor. Which has nothing really to do with robotics, even though your target application might be robotics.
Most designers can probably find an existing processor that will do most of what they'll ever need.
So I think you probably don't need an FPGA.
A starter roadmap: from commercial capabilities to (maybe) an FPGA...
First goal in my opinion is to try to get all of your creative concepts built up into a working robot (quite an intensive challenge in itself).
If you find that you've got specific and significant processing bottlenecks in your design, then the next goal is optimising the selection / design of your processors, still commercially available chips. Maybe bigger, faster (trade-off with power draw, heat dissipation). Maybe smaller, dedicated chips handling specific tasks and interfacing with the main brain (trade-off with algorithm / logic complications).
Only if there's capabilities that you just won't be able to get commercial chips to handle, then you might consider implementing a specialised processor inside an FPGA because at that point there will be very clear advantages that you hope to gain by 'rolling your own', and you can focus on just implementing those capabilities, with the right interfaces to rest of your design.
Otherwise, you're likely to get side-tracked from your main goal (which I'm going to assume is to actually build a robot!)
Bottom line: FPGAs are a distraction from getting started in robotics --- until you're quite a ways down the robotics road -- and have gained some strong chops in digital electronics / microprocessor design somewhere along the way.