grammaticality - Is this an appropriate usage of "but" at the beginning of a sentence?

Your example sentence has but for, which is a preposition, not a conjunction. So none of the so-called rules prohibiting starting sentences with a conjunction apply.

As the comments here and other answers to similar questions make clear, there are times when it is absolutely the best choice to start a sentence with a coordinating conjunction such as and, but, or.

Language Log has an excellent article on this, which contains the following text:

There is nothing in the grammar of the English language to support a
prescription against starting a sentence with and or but --- nothing
in the norms of speaking and nothing in the usage of the best writers
over the entire history of the literary language. Like all languages,
English is full of mechanisms to promote coherence by linking a
sentence with its discourse context, and on any sensible evaluation,
this is a Good Thing. Whoever invented the rule against
sentence-initial and and but, with its preposterous justification in
terms of an alleged defect in sentential "completeness", must have had
a tin ear and a dull mind. Nevertheless, this stupid made-up rule has
infected the culture so thoroughly that 60% of the AHD's (sensible and
well-educated) usage panel accepts it to some degree.

People who have internalised such zombie rules (Language Log) from school have maybe suffered from teachers who applied the "If they do it too much, they must be told not to do it at all" syndrome. In other words, elementary school students are told never to start a sentence with and to preclude typical narratives that are a string of "And then I did this ... And then I did that ... ." This is what people tend to remember, and not the more nuanced discussion that takes places (should take place) in high school English class.

Again, there is a helpful discussion of the above syndrome on Language Log.

As an aside, because is a subordinating conjunction, and there is never a problem starting a sentence with a subordinating conjunction, as long as the clause it begins is followed by a main clause - otherwise you have a sentence fragment. But, again, there is no prohibition on writing fragments. Because they can be the most effective way to make your point.