Relic Shield does not execute on Thresh because Thresh is a ranged champion in every single possible mechanic in the game.

Does relic shield still heal?

Relic shield healing decreased when proc'd by ranged champion. The new runes have given many ranged supports much higher poke damage in the early game, making it more punishable for Tanks to cash their Spoils of War stacks.

Is thresh auto ranged?

Thresh's auto attacks are considered ranged, because he has an attack range of 425. His auto attacks aren't blocked by Yasuo's Wind Wall because it is not a projectile, similar to Rakan's auto attacks.