Shadows in D&D are weird and quite varied across editions.
Basic, where undead explicitly make no noise, has them as not undead. OD&D has them as explicitly not undead as well. 4e puts them as shadow type and explicitly not undead too. AD&D-3e +5e has them as undead.
OD&D has them as non-corporeal. 2e talks about them throwing treasure in wells as if they were physical. It also has the weird alien creature shadow picture in both the MC and MM. 3e has them as fully incorporeal again but now flying for the first time. 4e they do not fly but they are insubstantial. 5e they don't fly and only makes them able to go through 1 inch openings without squeezing, they don't get the 5e incorporeal movement of things like ghosts and wraiths.
In 2e your body is gone once you get turned into a shadow, in 5e they separate on death/spawning and if the body is raised it does not have a shadow of its own until the spawned shadow is killed.
They generally have low intelligence but are not mindless. Generally this would indicate an ability to speak in a number of editions.
Their strength drain can be really deadly, particularly if you are facing a pack of these low level monsters (3e in particular). They are in the spawning can get exponentially apocalyptic real quick category of undead/monsters. In a number of editions they require magic to hurt them at all, in 5e 14 they just have resistance to nonmagic weapons and in 5e 24 no resistance, you can punch them for full effect.
I don't think there is any actual discussion of whether they can talk or not in their monster book entries. I am not familiar with any examples of them doing so in an adventure or sourcebook.