'In chess analysis, computer tools like Stockfish, Komodo, and AlphaZero help us know the importance of each chess piece during the game. They use calculations to assign a value to each piece based on factors like mobility, king safety, and board position...'(12 Sep 2023, Tato Shervashidze, Chess Coach...)

It is not only false, but it sounds like total nonsense to me. For one, AlphaZero is not comparable in any respect to Komodo or Stockfish; everything is different, and naming them in one breath already exposes the one who says this as completely ignorant on the subject of computer chess. (Which of course doesn't exclude he is a good Chess coach or has a high rating.)

In the past few years there has been a revolution in chess programming, after it had been converging to a method thought to be optimal for several decades. Initially programs were scoring positions at the leaves of a look-ahead search tree by a static (= not playing out any moves) heuristic that is now called a Hand-Crafted Evaluation. Piece values were a major part of that, often interpolated between 'opening' and 'end-game' values depending on the strength of the material still on board. The positional terms were Piece-Square Tables (accounting for mild general position dependence of piece values, without taking note of the location of other pieces, such as that Knights are poor at edges, and even poorer in corners), mobility (the actual number of moves a piece has in the current position), King safety (the number of squares around the King attacked by opponent pieces, and the value and number of these pieces), Pawn structure (passer advance, isolated / backward and doubled Pawns)

These parameters were never calculated (for orthodox Chess engines), but often were tuned. This was done by taking a large data set (like 500,000) of quiet positions from games with known result, and then tweeking all the bonuses and penalties (including piece values) that were used in the HCE until the calcuated evaluation score correlated best with the game result.

Than came AlphaZero out of nowhere, with everything completely different. It used a neural network for evaluation of positions as well as for guiding the search. This network simulates a brain with millions of cells, in some 40 layers, with tens of millions of connections between them. And they tuned the strength of those connections by having the thing play chess against itself. No one knows what each connection represents, but the result is that it eventually it could very accurately predict the winning probability for a position, apparently paying attention even to subtle strategic condiderations.

After that a hybrid form was invented: NNUE (for Easily Updatable Neural Network; no idea why they spelled it backwards...). This uses a conventional (unguided by any NN) search to calculate ahead, but at the end of each line evaluates by a NN of a peculiar design. It does not use explicit piece values, but calculates something very similar to Piece-Square Tables (which can be seen as a sort of piece values specified by location of the piece, and can simulate a plain piece value by specifying that same value on every square). Except that it does have such a PST for each location of the King. So the value of a piece cannot be dependent only on its absolute location, but also on how it is positioned relative to the King. (Well, this was invented for Shogi, and there proximity to the King is often more important than the intinsic strength of the piece type...). And it doesn't have one such a 64x64 table for each piece type, but 256 of them. And all these 256 values of each piece (on its current location, for the current King location) are than fed into a NN of 5 layers with 32 cells per layer, to combine them, until finally a single number appears at the output. This NN is then trained by tuning all the 256x64x64x6 values in the KPST, and the strength of the 4000 connections in the NN to reproduce the win probability of a huge data set of quiet positions, as good as it can.

This works, but after this no one knows what exactly the NN does. None of the values in the KPST in the optimally trained NN have the slightest resemblance to piece values as we know them. We cannot identify a King-Safety part, or a Pawn-Structure part, or a mobility part. It is just one totally integrated complete mess of totally meaningless multiplier parameters, that magically manage to conspire to give a very accurate prediction for who has the better winning chances in a given position. Stockfish and other strong engines now all use NNUE evaluation, (because they typically gain ~80 Elo compared to their original HCE), and the main development towards higher Elo comes from finding better sets for training it, or playing a little bit with the size of the NN. (Large NN can predict more accurately, but slow doen the engine, so that it cannot look as far ahead.)