Azure Security Center with Ubuntu 19
Problem solved, I think: the agent comes with its own libcurl.so.3 in /opt/oms/lib, it doesn't use the system one at all. Once I replaced that, it seems to be succeeding. Previously:

$ cd /opt/microsoft/omsconfig/Scripts
$ ./PerformRequiredConfigurationChecks.py
instance of OMI_Error
{
    OwningEntity=OMI:CIMOM
    MessageID=OMI:MI_Result:1
    Message=cURL failed to perform on this base url: uks-agentservice-prod-1.azure-automation.net with this error message: Stream error in the HTTP/2 framing layer. Make sure cURL and SSL libraries are up to date.
    MessageArguments={}
    PerceivedSeverity=7
    ProbableCause=0
    ProbableCauseDescription=Unknown
    CIMStatusCode=1
    OMI_Code=1
    OMI_Category=0
    OMI_Type=MI
    OMI_ErrorMessage=A general error occurred, not covered by a more specific error code.
}


But now:

$ ./PerformRequiredConfigurationChecks.py
instance of PerformRequiredConfigurationChecks
{
    ReturnValue=0
}