Learn German: So alt der Leuchtturm auch ist, der Wärter bleibt dort. - As old as the lighthouse is, the keeper stays there.

This structure translates to "However [adjective]" or "As [adjective] as". Here, So alt ... auch means "As old as..." or "However old...". It creates a concessive clause, which introduces a contrast similar to using obwohl (although). Because it is a dependent clause, the verb ist is pushed to the very end of that clause.

Why doesn't the main clause invert the verb and subject? Why is it der Wärter bleibt instead of bleibt der Wärter?

This is a special feature of so ... auch clauses! Usually, a dependent clause takes up "Position 1" and forces the verb to the front of the main clause. However, concessive clauses like this are often treated as "unintegrated" or structurally separate. As a result, the main clause simply starts over with standard word order: Subject (der Wärter) then Verb (bleibt).

Could I just use obwohl to mean the exact same thing?

Yes, but the emphasis is slightly different. Obwohl der Leuchtturm alt ist simply states a fact: "Although the lighthouse is old." The So alt ... auch structure strongly emphasizes the degree of the adjective, giving it the feeling of "No matter how old the lighthouse is."

What is the word auch doing here? Can I drop it?