That's not what the actual Russian-speaking people have been telling me here. I'll take the native-speakers' word for it when they tell me that all word-final consonants are unvoiced. Although yes, it is "soft"; the technical term is palatalized. It's a palatalized dental "t". IPA: [loʂət̪ʲ]. All word-final "д"s become "т"s, just as word-final "б"s become "п"s (like in хлеб, which is pronounced with a final "p" instead of a final "b"), and word-final "г"s become "к"s, and word-final "ш"s become "ж"s, and word final "з"s become "с"s. Many Russians don't consciously realize this about their own language, and this is one of the things that creates a Russian accent in English, when Russian-speaking people do this same thing in English, because it's subconscious for them.
It won't let me reply to your comment in the other sub-thread, so I'll reply to you here. You asked "“All word-final "д"s become "т"s” Really, all? Preceding consonants can't voice it?" To which my response would be that as far as I know, the answer here is no. Consonants do not determine the voicedness of the following consonant, but rather the previous one. For example, in "всё", the в does not voice the с, but rather the other way around. The с devoices the в.
You're welcome. Though I'd just like to stress once more that this is just "as far as I know". This is what it was saying in the Tips & Notes section of one of these sections. Although it's worthy of note that it didn't mention if the voicing assimilation works differently in word-final clusters. The lack of mention about that leads me to conclude that it doesn't, but just because it didn't mention a difference doesn't mean that there necessarily isn't one. However, that being said, I decided to look into this on Wikipedia before finalizing this comment, and my research there would suggest that I'm correct; it does not work the same way as it does in Polish.