Learn Swedish: Katedralens nya pelare är trettio meter höga. - The cathedral's new pillars are thirty meters tall.

Because it describes the plural subject pelare (pillars). In Swedish, when giving a measurement, the adjective comes after the unit of measurement (meter) and must agree in number with the noun it describes. So we use the plural höga rather than the singular hög.

Why don't we add an 's' to meter to make it plural, like in English?

In Swedish, units of measurement that are 'en' words usually do not change their form in the plural. So one meter is en meter, and thirty meters is trettio meter.

Why do we use the definite adjective nya but the indefinite noun pelare?

When a noun is preceded by a possessive word ending in -s like katedralens (the cathedral's), it triggers a special rule. The adjective takes the definite -a ending (nya), but the noun itself must remain in the bare indefinite form (pelare, not pelarna).

Could I use långa instead of höga to mean 'tall' here?

Not for a pillar. In Swedish, lång is used for the height of people (like han är två meter lång). For inanimate vertical objects like buildings, trees, or pillars, you must use hög.