Synapse just uses whatever libssl.dylib is pointing to.
So libssl.dylib should point to something that is OpenSSL "compatible" (which I assume LibreSSL/libssl.35.dylib is).
{$IFNDEF MSWINDOWS}
{$IFDEF DARWIN}
DLLSSLName: string = 'libssl.dylib';
DLLUtilName: string = 'libcrypto.dylib';
{$ELSE}
{$IFDEF OS2}
{$IFDEF OS2GCC}
DLLSSLName: string = 'kssl.dll';
Don't point to a specific version in your code, otherwise you'll end up changing it regularly.
B.T.W. What version is that libssl.35.dylib? I see that LibreSSL only goes up to 2.8.0.
Maybe it's a version which doesn't support the new TLS.
Edit: I see LibreSSL 2.5.5 has libssl-43.dll for Windows. So I guess libssl-35 is quite old.
libssl-35 seems to be from the 2.2.x branche which is from 2015, maybe 2016.
These might really have problems with the new TLS.
Try to find a newer LibreSSL version for your OS and install that.