What kind of spren is Oathbringer, the Shardblade?
Oathbringer is not technically a spren. Why I call these things the Honorblades, kind of where the whole Shardblade concept fits in, is that these are literally pieces of Honor's soul that he Splintered off and formed weapons out of for the Heralds. These didn't actually have sentience, in the same way that the spren forming most of the Shardblades are. They're literally a piece of the god who ruled this world turned into weapons. And the spren, who are also pieces of the same divinity, saw what was happening, and this kind of became a model by which Shardblades came about.
So Oathbringer doesn't have a spren. If you wanted to call it something, call it a sliver of Honor that has been manifested in physical form. That does mean the blade would actually be made of Tanavast's god metal, so tanavastium, if you want to call it that.
Yeah, that's just me hearing what I wanted to hear, not what was actually asked. It happens more often than I'd like; I get into this groove of answering questions, and start answering what I'm thinking about rather than what actually gets asked. A lot of times, I'm expecting a question (often because it's one that gets asked a lot, like what are Shardblades made out of) and my brain defaults to the answer I've prepared. I think it might be because I've trained myself to answer questions while doing other things.
Oathbringer's not an Honorblade. It was a Stoneward's blade a long time ago, with the corresponding spren.