I’ve never encountered anything like Egan before. I’ve heard Stanislaw Lem mentioned in conversations about him though. But I can’t vouch for the comparison myself as I’ve never read Lem.
Both are fresh voices and well worth reading, but I don't think Lem comes anywhere near Egan's diamond-hard sci-fi. Egan knows, and does, real math; you can sometimes find him at the n-category Café. My impression is that Lem's beautiful philosophical ideas were not accompanied by comparable math or physics knowledge.
Lem is humanist. The sci-fi part is only a vehicle to make you think (eh, if you want to), and while things are written in 1950-80... they are not outdated, because humans are essentially same, for millenias. Just read "Stories of commandor Pirx". Somewhere in the middle of them, you may notice something like the current frenzy around LLMs and ethics. But he goes further..