Maybe you could engrave the relative positions of some nearby stars onto a plaque or something like that? Ceramic lasts basically forever, right? Maybe you wouldn’t get “Tuesday, Deceduary 110th 2132” level of precision but you could perhaps get something pretty precise with the right choice of stars?

We know what the positions of those stars were back into the ancient past and forwards into the distant future. We can engrave positions corresponding to any date we like onto such an object. It provides no proof of date.

There's no need. All of our biological waste (e.g. wood) will provide reliable carbon dates within the range of ~50k years. Radioisotope ratios in our metals and construction materials can be used to date our inorganic ruins on geologic time scales.

Radioisotope dating doesn't work for stone structures like the one described in this article, because it would date the age of the stone, not the structure. But concrete is poured, and steel forged or reforged at or close to its actual use date. So radioisotope ratios in these materials ought to give a reliable dating mechanism on very long timescales.

Someone could put hermitically sealed cartridges of something that will decay nicely into a high visibility container that's designed to stay permanently built into the structure itself. Future humans could drill through the solid exterior and retrieve samples of the decaying inner material providing definitive means of precisely dating the structure. Designing it to be used more than once by successive generations would help keep future history more accurate than ancient history.

Why bother? Radiocarbon dating is only good up to about 50k years. Longer than that and you would use longer lived radioisotopes which are in the construction materials anyway.