we own the domains page.et and suk.et, purchased at Ethio Telecom, with DNS hosting managed at Cloudflare and successfully got a letsencrypt wildcard certificate.
PS: Ethiotelecom is selling both, second level domains, but also third level domains (under .comt.et, .net.et) an such. Second level domains became available since not so long ago (something between 9-12 years ago, I guess). Maybe that's related?
Uh, yes. The CAA record for .et allows several CAs (including Let's Encrypt) for non-wildcard, but only Sectigo & Digicert for wildcard. Very, very weird for there to be a CAA record on a TLD, and is likely the first time that has happened.
You should be able to set a CAA record for the names you control directly, at page.et and such, for the CAs which you want to use.
There's an article published by APNIC that says as of May 2023 no TLD had one set. That's part of why I said this was probably the first. While I could imagine a TLD that legitimately had one (like the actually-owned-by-a-company TLDs of .google and .apple and such), I really wouldn't expect a country code TLD to have one.