Sorry for the previous posts.
It just turns out that something may have been up with Chrome on Windows.
On September 6, they released a new version 117, where they disabled SHA-1 fingerprint, and since then I've had problems with the token on Let's Encrypt certificates with ECC 384bit.
Only today after updating to version 118, it just started working as it should properly even in the „Enchanced protection” mode in the security built into Chrome.