Technically, this isn't a complete sentence, precisely because it lacks a main verb. When you pare this text down, omitting unneeded complications, it reads:
the government's strategy of using this moment to not X, but rather to Y.
This makes it clear that what we have here is a descriptive phrase, one with lots of complications inside X and Y. To make it a full sentence there would need to be a verb, One could either add a verb on the end that said something about what the described strategy was, or was doing. Or, perhaps better, it could be changed to:
the government's strategy is one of using this moment to not X, but rather to Y.
That would still be an overly complicated sentence, but now a full sentence.
Oh, in the expression
.. to not paper over any cracks that may have appeared ...
the clause headed by "that" modifies "cracks" describing what sort of cracks the author means.
It is possible in a few cases to have a sentence wiuth no verb at all. For one example, direct answers to to questions are generally considered full sentences, even if shortened to omit the verb. for example:
A: Are you coming tomorrow?
B: Yes!
A: What time?
B: 7:00 pm
B's answers are sentences., Ofg course they are short for "Yes I am" and "I will arrive at seven pm" or something similar.
It is also possible to construct pathological sentences where a verb is implied but not stated, such as the well-known example of:
This sentence no verb.
where the verb "has" is implied. I would not advise using such sentences in normal speech or writing.
But aside from shortened sentences, and ones with implied verbs, I think that every sentence requires a main verb. Some might argue that the above examples are not truly complete sentences.