OpenSSL cipher suite support / key requirement for ecdhe_ecdsa_with_aes128_cbc_sha256
Why does the server say there was no shared cipher when I explicitely set up the server to support only that one cipher suite?

The chosen cipher suite requires that an ECC certificate gets used. Likely you have a RSA certificate instead since most instructions on how to create a certificate cover only this. If you have a RSA certificate you cannot use an ECDSA cipher and thus the server has essentially no cipher to choose from - which results in no shared cipher.

How can I make this work?

Create an ECC certificate for the server. See for example Create a self-signed ECC certificate for instructions.