Does Sigil of the Storm force you to use runes, or does power like seals/Jhin work?

No. You must recycle an actual rune card from your rune deck or board. Seals, Jhin's cost reduction, or any other way of generating Power does not satisfy it.

Sigil of the Storm says "you must recycle one of your runes" — that's a specific game action, not a Power cost. Exhausting a Seal or getting a discount from Jhin produces or saves Power, but neither performs the action of recycling a rune. The FAQ is firm on this: Seals cannot pay for it (FAQ #8821, #6663), and exhausting a Sigil (a rune gear) to float Power is also not recycling a rune (FAQ #6273).

One edge case: if you have zero runes in your rune deck and on board, the effect triggers and does nothing — you still conquer and score (FAQ #6863). But as long as you have runes available, you must recycle one.