Did Tony become worthy when he chose to sacrifice himself?

I really don’t think so.

The reason is that it’s not enough to have the will to sacrifice one’s life to become worthy, which Tony Stark has even done more than once.

At the end of Avengers he was willing to sacrifice himself to bring the atomic bomb inside the portal, but he survives.

So, even if the intention to sacrifice was there, we know from Age of Ultron, obviously set after the battle of New York, that he is completely unable to move Mjölnir.

It could be argued that Mjölnir may not have taken Stark seriously given that it was a simple challenge between friends, but that doesn’t hold, since both Thor and Cap managed to move it (Cap just stopped).

Tony’s sacrifice in Endgame may somehow have more “value” than New York’s one, because the whole universe was at stake and Tony, who expressly didn’t want to die, ultimately really gave up his life.

But even here, the matter is not so simple: Tony could have sacrificed himself just to save his daughter. Even a sacrifice can have selfish components, and Mjölnir can probably sense that.

So no, Endgame’s sacrifice didn’t make him worthy. Only very few individuals (preferably warriors) with exceptional selflessness, moral integrity and humility can lift Mjölnir. And those aren’t exactly Stark’s qualities. It’s not a single action, no matter how good, that makes you worthy.

Even assuming he had become worthy, it is not sure that the hammer would rush to him. What would compel it to do that? The only character Mjölnir is particularly attached to is Thor, and no one else is ever seen using Mjölnir to come back to life. Not even Captain America wounded by Thanos is healed by the hammer.