Why does chewing gum sometimes change its texture

The cookies will set (take on their final texture) about by 20 - 30 minutes out of the oven. Coming directly out of the oven, cookies will absolutely be soft and squishable; which is why you should wait a few minutes before moving them off the baking sheet and onto a cooling rack (you can cheat this time if your cookies are all on a sheet of parchment paper, and you move the parchment paper as a whole).

Yes, there are two different meanings of taste, as you already mentioned. One is the salty-sweet-etc. multidimensional space of sensory perceptions felt with the mucous membranes of the mouth (many authors add astringency and pungency/hotness, which are not felt by the tastebuds themselves), and the other is the overall impression of the food. The overall impression includes also the aroma - citric acid and acetic acid in a solution at the same pH level are both equally sour, but you can tell them apart by aroma - and the texture. An example for the texture would be to try confectioner's sugar and pure rock candy - both are 100% sucrose, so have the same narrow-meaning-taste (sensory perception of sweetness), and both have the same aroma (provided they are produced from the same plant at the same degree of refinement, which is often the case with white sugar), but your overall feel of them (taste in the broader sense) will be entirely different due to the different texture.

Taste in the narrow sense can also be slightly different with different texture, due to the difference in availability of the taste-creating chemicals to the taste buds (and to the rest of the mucous membrane). The obvious difference comes with density. Cotton candy does not feel as overpoweringly sweet as the same volume of table sugar, because it is mostly air and doesn't trigger as many taste buds at once as the sugar. This is a difference in the strength of taste, not in the taste profile - cotton candy doesn't start tasting more-salty-than-sweet due to the different density, it just tastes less sweet.

Another thing which might happen to taste is that the structure which creates the different structure isolates some of the taste-causing molecules from the taste buds. I know from experience that this happens with aroma. Adding xanthan gum to food reduces its aroma, I assume that it traps the volatile molecules which would normally reach the olfactory sensory cells. But if it does reduce the taste too, it doesn't do so in the same proportion, as there is much more taste left than smell. If somebody knows for sure that it reduces the strength of taste too, I would like to see conclusive information on it; I only include it here as a hypothesis.

Summary, texture changes taste in both the narrow and broad sense. It does so more strongly for the broad sense, which is the one most people care for.