If you wish to cast the exiled card, you do so as part of the resolution of Transcendent Dragon’s last ability. You can’t wait to cast it later. Timing permissions based on the card’s type are ignored.
2025-04-04
If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs those must be paid to cast the spell.
2025-04-04
If a spell has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
When this creature enters, if you cast it, counter target spell. If that spell is countered this way, exile it instead of putting it into its owner's graveyard, then you may cast it without paying its mana cost.
in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.