Learn Portuguese (Portugal): Os vizinhos estão a incomodar-me.

This sentence shows the default rule. Because there is no "magnet" word in this sentence (like an adverb or an indefinite pronoun), the pronoun does not move to the front. Instead, it attaches to the end of the verb with a hyphen.

How would the pronoun placement change if we added an adverb like sempre (always)?

Adverbs act as magnets and pull the pronoun before the first verb. If you added sempre, the sentence would become Os vizinhos sempre me estão a incomodar. The me jumps before the verb estão to stay close to the magnet word.

Could I attach the pronoun to estão instead, like estão-me a incomodar?

Yes! In European Portuguese, when you use the estar a + infinitive structure, you have two choices when there are no magnet words. You can attach the pronoun to the helping verb (estão-me a incomodar) or to the infinitive (estão a incomodar-me). Both are perfectly correct.

I remember that estar a plus the infinitive means doing something right now. Is that what is happening here?

Exactly! The phrase estão a incomodar uses the verb estar (to be) followed by a and the infinitive incomodar (to bother). This is the standard way to say "are bothering" (the present continuous tense) in European Portuguese.