Is the T silent or not?
That’s a good question. You always ask such good questions.
The simple answer is, you can pronounce it either way. Often developed from oft, probably due to its relation to the related word seldan, which developed into seldom. Originally the T was pronounced in often, as it was pronounced in oft.
Meanwhile, around the 16th century, -en began to be added to a variety of words to make verbs, such as fasten, hasten, or soften. At first, these T‘s were pronounced, but at about the same time, the pronunciation of words with consonant clusters began to be simplified. Because all those consonants together can be cumbersome. This is evident in the silent letters in words like handkerchief, castle, handsome, and raspberry, as well as the words ending in -ten words above.
This is why the T in often also became silent. However, because it had so recently come into use, and people were still using oft, the T continued to be pronounced by some, as it is to this day. It’s still more common to pronounce the word with a silent T, and it generally sounds a little more formal to pronounce it, but you can go with either.