Are you referring to making an OpenSSL-compatible API, so OpenSSL-only programs can link against BearSSL?
I really like BearSSL for TLS 1.2: it’s tiny, runs well on old hardware, and has no dynamic memory allocation. I do have serious doubts for making it the default TLS library when it doesn’t support TLS 1.3. Looking at commit logs, I doubt it’ll get 1.3 anytime soon.
mbedTLS, LibreSSL, WolfSSL, s2n-tls, MatrixSSL, GnuTLS (eww), BoringSSL, picotls, NSS, even Fizz and Rustls (just including these two for completeness) all support 1.3 and can be linked in C programs; picking the one high-profile implementation lacking it seems like a bad idea. Perhaps wrapping BearSSL and a TLS 1.3 implementation (like picotls) could work?
Personally, I’d like to see adoption of more 1.3 extensions to reduce information leakage, such as Encrypted Client Hello or random padding.