The u is pronounced, but it’s a shorter sound than English u. Vowels in Japanese are shorter than English ones, which makes sense for a language where vowel length matters, eg su (vinegar) is a different word than suu (to smoke).
I’m trying to think of a word that wouldn’t use u as an insert between 2 English consonants, like trip becomes torippu, but that’s probably because they wanted to avoid tsurippu, as you mentioned about tsu. One word is garasu meaning glass (the material), but they also have gurasu, meaning drinking glass.
Most words do tend to use the u between English consonants though (supo-tsu, purezento, surippa, sute-ki, etc).