"Biological products include a wide range of products such as vaccines, blood and blood components, allergenics, somatic cells, gene therapy, tissues, and recombinant therapeutic proteins. Biologics can be composed of sugars, proteins, or nucleic acids or complex combinations of these substances, or may be living entities such as cells and tissues. Biologics are isolated from a variety of natural sources - human, animal, or microorganism - and may be produced by biotechnology methods and other cutting-edge technologies. Gene-based and cellular biologics, for example, often are at the forefront of biomedical research, and may be used to treat a variety of medical conditions for which no other treatments are available."
"a semi-synthetic drug substance is one in which the structural constituents have been introduced by a combination of chemical synthesis and elements of biological origin (e.g., obtained from fermentation or by extraction from botanical material)."
https://www.fda.gov/media/80909/download
Based on this document "List of Withdrawn Applications for Biological Products That Were Removed From FDA’s Orange Book on March 23, 2020" we can say that semi-synthetics are a subgroup of biologics. In the document which covers 'Withdrawn Applications for Biological Products' in four places, FDA mentions semisynthetic insulins ....
https://www.fda.gov/media/136420/download
Moreover, ICH not includes semi-synthetic into 'synthetic drugs', see an example:
"This document is intended to provide guidance for registration applications on the content and qualification of impurities in new drug substances produced by chemical syntheses and not previously registered in a region or member state. It is not intended to apply to new drug substances used during the clinical research stage of development. The following types of drug substances are not covered in this guideline: biological/biotechnological, peptide, oligonucleotide, radiopharmaceutical, fermentation product and semi-synthetic products derived therefrom, herbal products, and crude products of animal or plant origin."