Learn Hardcore German: Unser Chef fragte, worauf wir stolz seien; ich antwortete, dass die stabile Verbindung zur Datenbank unser größter Erfolg sei. - Our boss asked what we were proud of; I answered that the stable connection to the database was our greatest success.

worauf is a fused preposition (Präposition plus interrogative pronoun) used in indirect questions. In direct speech you’d ask „Worauf seid ihr stolz?“ rather than „Auf was seid ihr stolz?“, because worauf is stylistically preferred over auf was. In indirect speech after fragen, you retain worauf, shifting to: „Unser Chef fragte, worauf wir stolz seien.“

Why is wir stolz seien in the subjunctive (Konjunktiv I) mood rather than indicative?

German uses Konjunktiv I in reported (indirect) speech to mark that you’re reporting someone else’s words or questions. Here „Unser Chef fragte, worauf wir stolz seien“ literally means “Our boss asked what we were proud of,” and sei is the Konjunktiv I form of sein for wir. It distinguishes the report from a direct statement (wir sind stolz).

Why does the verb sei appear at the end of the clause dass die stabile Verbindung ... unser größter Erfolg sei?

In German subordinate clauses introduced by conjunctions like dass, the finite verb moves to the final position. So you get dass … sei rather than … sei, dass … This is a core rule of German word order for Nebensätze (subordinate clauses).

When do you use dass versus dass with the subjunctive? And why is sei used again?

You use dass to introduce subordinate clauses that function as objects, facts, or explanations. When reporting your own answer indirectly after antwortete, you still use Konjunktiv I (sei) to mark indirect speech: „ich antwortete, dass ... unser größter Erfolg sei.“ If you were making a direct statement, you’d say „Die stabile Verbindung zur Datenbank ist unser größter Erfolg.“

Why is it zur Datenbank instead of zu der Datenbank?

zur is a contraction of zu der (Dative feminine singular). In everyday and formal German, common preposition + article pairs like zu + der = zur are usually contracted. The meaning doesn’t change.

Why is the adjective stabile not stabilen in die stabile Verbindung?

This is a case of weak adjective declension. After the definite article die (feminine, nominative), attributive adjectives take the ending -e in singular:
die (article) + stabile (weak ending -e) + Verbindung (noun).
If it were eine stabile Verbindung, you’d use the strong ending -e as well, but if the article indicated a different case or number, endings would shift accordingly.

How is unser declined in unser Chef?

Unser is a possessive pronoun behaving like an adjective. Here Chef is masculine, nominative singular. Possessive pronouns before a noun with a definite sense take the same endings as the definite article in weak declension—so unser remains unchanged for nominative masculine:
unser (no ending) + Chef.

Why is there a semicolon between the two clauses instead of a comma or period?

The semicolon here links two related main ideas: the boss’s question and the speaker’s answer. A comma would be too weak for two independent clauses without a conjunction; a period would separate them more strongly. The semicolon shows a close connection in a stylistic, formal register.

Could the sentence be split into simpler sentences? If so, how?

Yes, for clarity you might use two sentences:

Unser Chef fragte, worauf wir stolz seien.
Ich antwortete: Die stabile Verbindung zur Datenbank ist unser größter Erfolg.
Here you switch back to direct speech for the answer or use a colon to introduce it.