I don't think you understand what's happening. Amazon's algorithm is not just increasing price to match competitors. They are temporarily increasing price beyond competitors to see if competitors will also increase their price. This is different because there is no original market force impetus for the price increase, they are just seeing if both they and a competitor can coordinate to make a permanent price increase.

Arbitrarily interesting a price to see if you're competitors will also increase is not adjusting to market competition. It's testing the waters for colluding on price. It's literally sending a signal that Amazon is willing to increase if others will match. Whether the agreement is made in secret or done in public using "plausibly deniable" price increases makes no difference.