Learn German: Wir tragen standardmäßig schwarze Schuhe im Büro. - We wear black shoes in the office by default.

It combines the noun Standard with the suffix -mäßig. This suffix generally means "in the manner of", "in terms of", or "according to". Here, it creates a word that translates perfectly to "by default".

Is standardmäßig functioning as an adjective or an adverb here?

It is acting as an adverb because it modifies the verb tragen (telling us how we wear them), which is why it doesn't take any adjective endings. If it were describing a noun directly, it would need an ending, such as in die standardmäßigen Schuhe (the default shoes).

Why does the adjective in schwarze Schuhe end in -e instead of -en?

This is a refresher on strong adjective declension. Schuhe is the direct object (accusative plural), and there is no article like die or meine in front of it. Without an article to show the case, the adjective schwarze has to do the heavy lifting by taking the strong plural ending -e.

Could I put standardmäßig at the end of the sentence?

It is much better where it is. In German, adverbs of manner (how something happens) usually come before the direct object when that object is a noun. It sounds unnatural to put it at the very end of this sentence.