Learn Croatian: Novi pod je sjajan. - The new floor is shiny.

Because it comes after the verb je (is). When an adjective describes a noun but is separated by the verb 'to be' (acting as a predicate), Croatian prefers the indefinite form. That is why it drops the final -i and uses sjajan.

Why do we use novi at the start instead of nov?

Novi is the definite form, meaning 'the new...'. If you used the indefinite nov, it would mean 'a new...'. Since we are talking about a specific floor, the definite form novi pod is the natural choice before the noun.

How would this sentence change if I wanted to say 'Everything is shiny', using the pronoun sve from this lesson?

You would say Sve je sjajno. The word sve (everything) is treated as a neuter singular subject, so the adjective must match it by taking the neuter ending -o instead of the masculine indefinite -an used for pod.

I have seen sjajan used in a different context. Does it only mean 'shiny'?

No, it has a very common second meaning! While it literally means 'shiny' or 'radiant' (from the noun sjaj, meaning 'shine'), Croatians frequently use sjajan to mean 'great', 'awesome', or 'brilliant' (for example, sjajna ideja means 'a brilliant idea').