there's a hint that you are misunderstanding how things work a bit here. By the time you get to the footnote: "Unless you implement a CPU on top of the FPGA :)" you realize that of course FPGAs can be turing complete, but it's not really correct to say "on top of", more correct with be to say "implement a CPU with the FPGA. Secondly, you never say a CPU isn't really turing complete (footnote: unless you use JMP instructions). We would typically class machines class using the maximum possible because it's usually trivial, but uninteresting, to, for example, program or limit a Turing machine to not be Turing-complete.
Your other footnote is spot-on. I refuse to consider CPUs to be Turing complete (out of pedanticism) because given physical memory constraints. Realizable physical computers are, like all digital logic circuits) actually Finite State Machines with just really, really big state space (like 2^(~10^15) states). If you put every single flip-flop and DRAM bit back the way it was and execute the next clock, it will deterministically follow the same pattern. They aren't even PDAs (Push-Down-Automatons). EVERYTHING is an FSM (pedantically). Turing machines and PDAs are theoretically useful models for theoretical computer science and math, however. But not technically accurate.
FPGA's aren't CPUs that lack instruction pipelines. They are universal ASICs and/or digital circuits that are re-programmable. ANYTHING that can be accomplished with synchronous (clocked) digital logic circuit can be implemented with an FPGA, including CPUs, but also potentially many, many, other things.
Your other footnote is spot-on. I refuse to consider CPUs to be Turing complete (out of pedanticism) because given physical memory constraints. Realizable physical computers are, like all digital logic circuits) actually Finite State Machines with just really, really big state space (like 2^(~10^15) states). If you put every single flip-flop and DRAM bit back the way it was and execute the next clock, it will deterministically follow the same pattern. They aren't even PDAs (Push-Down-Automatons). EVERYTHING is an FSM (pedantically). Turing machines and PDAs are theoretically useful models for theoretical computer science and math, however. But not technically accurate.
FPGA's aren't CPUs that lack instruction pipelines. They are universal ASICs and/or digital circuits that are re-programmable. ANYTHING that can be accomplished with synchronous (clocked) digital logic circuit can be implemented with an FPGA, including CPUs, but also potentially many, many, other things.