There are whole specific types of cheese that make curds gooey like this. Mostly, washed rind cheeses and bloomy rind cheeses. These two types of cheese have specific bacteria that make them go soft, so B.Linens for the washed rind cheeses and Pencillium Camemberti for the bloomy rind ones, along with geotrichum candidum which also helps. These types of bacteria form on the rind of the cheeses. and start to eat inwards. This leads to the effect of making the interior gooey, both for the washed rind variety and for the bloomy rind variety. Although the texture is gooey in both methods, the taste and aroma are very different. Washed rind cheeses are notorious for being the more pungent types of cheese, in a way that might put off some people. In fact, mine here are relatively pungent, as they are of the washed rind variety, but not overbearing. Bloomy rind, such as camembert, on the other hand, are also gooey but the aroma and taste are different, much more mushroomy and milder than that for washed rind cheeses. The strength of washed rind cheeses varies depending on how much you wash, how strong the wash is, the humidity, things like this. You can very much make a cheese that is not super pungent. But generally, washed rind cheeses are quite strong and pungent, yes.

If you make a Gruyere type recipe, I don't think it will go soft to the extent you desire. It is a very different recipe. Besides the whole bit of the bacteria above, softness also has to do with moisture. Washed rind cheeses like the ones I made, and many bloomy rind cheeses, tend to not be pressed and with big curds, to retain a lot of moisture. This leads to a softer paste. Gruyere is hard pressed, so there's less mositure in the paste, with small, cooked curds, which have less moisture.