Why is "loosely" divided into syllables as "LOOS-LEE" and not "LOO-SLEE"?

It's because when you're dividing into syllables, morpheme boundaries often overrule the maximal onset principle. In fact, you can tell that the /s/ belongs to the first syllable because the vowel in loosely is shorter than that in loser, and vowels in syllables that end with a voiceless consonant are shortened in English.

This doesn't always happen. In the word waitress, the root word is obviously wait, so you might expect the syllable division to be after the /t/. But the pronunciation in Cambridge Dictionary is /ˈweɪ.trəs/, showing that in this case Maximum Onset Principle has overruled the morpheme boundaries.

The Maximal Onset Principle is a common idea about how syllabification should work, but in many contexts, there isn’t much evidence that it is how syllabification really works.

In fact, it’s difficult to get evidence for syllabification in general. Aside from native speaker intuition, which does not always agree, the indirect evidence used to argue for syllable division can often be interpreted in ways that don’t require reference to the concept of the syllable. Some linguists are skeptical or agnostic about the linguistic reality of syllable division.

In English, specifically, the Maximal Onset Principle seems to fail in two ways that are relevant to “loosely”:

1. Morphological division. As Peter Shor mentioned, syllable boundaries seem to coincide in some, but not all cases with morpheme boundaries, like the boundary between the base loose and the suffix -ly.

2. Stress attraction. While not accepted by all phonologists, there is a notable theory that consonants and consonant clusters in English are preferentially syllabified with stressed syllables (with some phonotactic restrictions), even when occurring between vowels. One of the most notable articulators of this theory is John Wells. In Wells’ theory of syllabification, loose.ly, waitr.ess, and self.ish are syllabified based on this phonological criterion; in contrast, words like shell.fish are syllabified based on morphology according to Wells (“Syllabification and allophony", 1990).