Learn Hardcore Turkish: Evli komşularımız kiracıya sıcak çorba verdiler. - Our married neighbors gave the tenant hot soup.

Evli means "married" and functions as an attributive adjective modifying komşularımız. In Turkish, adjectives come before the nouns they modify, so evli komşularımız means "our married neighbors."

How is komşularımız formed, and why is the plural before the possessive?

It’s built as: komşu + lar + ımız = neighbor + plural + our = "our neighbors."

In Turkish, the order is root + plural + possessive.
Vowel harmony applies: after -lar, the possessive becomes -ımız (not -imiz), because the last vowel before it is the back vowel a.
Without the plural: komşumuz = "our neighbor."
You can add the pronoun for emphasis: Bizim komşularımız = "our neighbors (as opposed to someone else’s)."

Why is the verb verdiler plural? Could it be verdi instead?

verdiler = ver- (give) + -di (simple past) + -ler (3rd person plural), matching the plural human subject komşularımız.
With an overt plural subject, Turkish allows both plural and singular verb agreement: Evli komşularımız ... verdi is also grammatical.
Using -ler with human subjects often emphasizes the plurality or adds a slightly more formal/explicit tone. With non-human plural subjects, the singular verb is more common unless you personify them.

What does the ending in kiracıya do, and why is it -ya not just ?