My reply is by no means an answer to your question. However, I still would like to drop in my 2 cents.
The notion of "quantum-inspired" algorithms has no formal definition and has a rather broad and interpretable meaning.
I've seen some papers that called their work "quantum" just because some classical part of their algorithm was remotely "inspired" or "motivated" by some quantum process. See this for example. The authors pitch their classical algo as "quantum-based".
Now, there are more "quantumy" classical algorithms which actually attempt to solve problems by classically simulating/approximating quantum processes. A good example would be a Simulated Bifurcation Machine. This is a more "quantum-inspired" algo than my first reference. The machine actually works and can handle complex problems. A number of people in the industry work on different hardware- and software-based implementations.
Then, there is, of course, Digital annealing, which is inspired by D-Wave's Quantum annealing. Basically, it is another CMOS-based Ising machine. It was tested and benchmarked. The thing seems to work alright.
We also have quantum-inspired graph neural networks for solving combinatorial problems. In this work, quantum-inspiredness is reflected in the treatment of a neural network. The neural network is conceptualized as an ansatz. According to the results in the paper, it works and can generalize to larger problems. But overall, it seems a bit impractical.
Also, the references in the OP post suggest that we can cook up "quantum-inspired" algorithms by introducing some concepts from quantum theory and then adding randomness together with sampling techniques. It seems like a good general recipe, and all the references above support this idea.
Some quantum algorithms can be simulated efficiently on classical hardware (Gottesman-Knill theorem). So any such a quantum algorithm can be "retailored" into a classical algorithm and branded as "quantum-inspired".
Overall, the concept of "quantum-inspired" algorithms is no different from the concept of "biologically-inspired" algorithms (e.g. evolutionary and swarm algorithms, neural nets etc) or any other "X-inspired" stuff. If you are very creative... You can come up with biologically-quantum-inspired algorithm... Again, see my first reference for that kind of stuff.
Although my answer is heavily biased toward optimization problems, hopefully, I could convince you that the word "quantum-inspired" is used quite liberally and sometimes intentionally misused for various reasons. Also, it is worth pointing out that the majority of "quantum-inspired" algorithms are heuristics and, as a result, possess many trade-offs.
