The grammatical parts of " instead of getting"

How would you analyze the gramatical form of the bold part of this sentence:

A significant number of people try to catch up on their sleep at the weekend instead of getting enough sleep during the week.

I think this is a prepositional phrase made up of a preposition (instead of) and a verb in its -ing form (getting). Or is getting a gerund? I am not entirely clear on the difference or if there is a difference.

edit: to clarify, this is an exercise that I have been assigned, the three words in bold need to have their form analyzed. So the focus of the first part of my question is not on the meaning, but on form (prepositional phrase: preposition + -ing verb or gerund). My question is really if you agree that it is 1) a proepositional phrase and 2) if the second half of the prepositional phrase is an ing verb form or a gerund (as I'm not clear on the difference, if there is). The second half of the question focuses on the "meaning" of instead of getting in this sentence. I based my answer on this entry https://dictionary.cambridge.org/grammar/british-grammar/prepositional-phrases?q=Prepositional%2Bphrases

I would also like to ask if this description of the meaning in this context is adequate:

The author uses the expression instead of getting to refer to one action (sleeping more on the weekend) replacing another (getting enough sleep during the week). In other words, the interviewed subjects try to catch up on their sleep on the weekends in lieu of obtaining enough sleep during the week.

edit 2 I've changed my meaning to the following: The author uses the expression instead of to contrast between one action that the interviewed people attempt to make happen (sleep more on the weekend) from another that does not happen (getting enough sleep during the week). In other words, the interviewed subjects attempt to catch up on their sleep on the weekends and they don’t get enough sleep during the week.

edit 3 I've changed my form analysis to the following:

Instead of getting is a prepositional phrase, consisting in a preposition (instead of) followed by a verb in its gerund form (getting, the -ing form of the verb get), which is the first part of the verb phrase (getting enough sleep) that is the object of the preposition.

Solution 1:

The whole phrase headed by the word instead is:

• instead of getting enough sleep during the week.

We can show here that the two words instead and of are not one word, but two. To show this we can put an adverb between them:

• instead, simply, of getting enough sleep during the week.

In the phrase above, we see the word simply interpolated between instead and of, demostrating that they are two words.

In modern grammars, such as Oxford Modern English Grammar (Aarts, 2011), prepositions can take a wide variety of Complements and other dependents, or may take none at all. Typically they take noun phrases, but they may also take clauses, or other preposition phrases.

In this particular case, the preposition instead is taking another preposition phrase as it's Complement. The complement preposition phrase is:

• of getting enough sleep during the week.

Here we have the preposition of taking the gerund-participal clause getting enough sleep during the week. The Original Poster asks whether getting is a an -ing form of the verb or a gerund. Well, even for those old-fashioned grammarians who favour nineteenth century grammar, both participles and gerunds are verbs. We can tell that the word getting is a verb here, because it takes a Direct Object. Nouns cannot do this, instead they put the equivalent of the Direct Object in a preposition phrase, typically beginning with the word of. Consider:

• The Vogons emancipated the Daleks.
• the Vogon's emancipation of the Daleks.

For such grammarians the verb getting is a gerund in the Original Poster's example because it is the Complement of a preposition. For modern grammars such as The Cambridge Grammar of the English Language, the distinction between gerund and participle is spurious because it is based on the words grammatical relation—for example, Complement of a preposition— and not on inherent properties of the verb itself. For this reason, they, and other modern grammarians, refer to such forms of verbs as gerund-participles regardless of their grammatical relations.

So, in short, the word instead is a preposition, taking a preposition phrase as a Complement. This preposition phrase is headed by the preposition of, which in turn is taking a gerund-participle clause as a Complement.