The Sagrada Família is a "recently" built cathedral, and I'd say is on a similar level as a Gothic cathedral. So modern society is not necessarily incapable of similar feats.

Yes, I’d agree with this. I’d almost say it’s the exception that proves the rule - it’s such an exceptional project in the modern sense that its presence highlights the absence of others.

I suppose things like the Svalbard seed vault are similar secular efforts, as is the Long Now’s clock, although that feels somewhat more self-indulgent than these others. I’m interested in others, if you can think of them.