indentation

maybe change this to:

auto isTransientError = [] (PackageKit::Transaction::Error error) {
  return (error == PackageKit::Transaction::ErrorFailedInitialization) ||
         (error == PackageKit::Transaction::ErrorNoNetwork) ||
         (error == PackageKit::Transaction::ErrorCannotGetLock);
};
...
if (failCount <= 1 && isTransientError(error) {
  ...
}

void function with return value.

The second parameter is missing documentation.

Can you make at least the second parameter an enum, e.g. RefreshReason::Manual, RefreshReason::Automatic.

Even with a comment I find it hard to read - is false /* manual */ the same as 'manual == false' or 'automatic == false, thus manual'.

The first parameter should IMHO also be an enum, but I have not checked if this broke API/ABI.

Returning void explicitly is just fine :-) I'll remove it though.

This lib isn't public (or at least not supposed to be used), so ABI/API breakage doesn't really matter.

I'll just add documentation, once the next option gets added I'll convert it into an enum.