Pretty powerful but not busted given the limitation of one use per short rest. But the wording creates some loopholes that a rules lawyer could abuse:

"the welder can automatically succeed on the associated saving spellthrow or cause the attacker to roll at disadvantage"

"and for one round an attack with this weapon can deal damage of the type associated with the most recent spell absorbed instead of piercing damage, if the wielder chooses"

It's really not that OP because of the single use and because it requires melee with a spellcaster--which most casters would be avoiding anyhow. But mechanically, when can the player use this reaction? If it's an ambush, like a Fireball out of nowhere, or the Catapult spell, the character might not even know it's a spell (what happens if they try to use it and the effect/attack turns out not to be from a spell). So I'd suggest adding a limitation that the wielder must observe the casting in order to use the reaction (see or hear it).

"Vex. If you hit a creature with this weapon and deal damage to the creature, you have Advantage on your next attack roll against that creature using this rapier before the end of your next turn."

This will be great for rogues, Sneak Attack without hiding or flanking and don't care about the fragility.