TCoE's Rune Knight fighter subclass gains proficiency in smith's tools (i.e. metalworking), and its first major feature is called Rune Carver, which says:
...you can touch a number of objects equal to the number of runes you know, and you inscribe a different rune onto each of the objects. To be eligible, an object must be a weapon, suit of armor, a shield, a piece of jewelry, or something else you can wear or hold in a hand.
The association with smithing, the use of the words "carver" and "inscribe," and the specific examples chosen suggest that the runes must be carved into a substance like wood, metal, leather, or stone. However, nothing in the rules' mechanics seems to truly constrain this. The criterion that the object must be something "you can wear or hold in a hand" is quite broad.
Can you touch an object that's wearable or holdable but unable to be carved (like a sheet of parchment or a linen shirt) and still cause the rune to be magically "inscribed" on it?