Please refer to this thread for a related question. Although the SBTi does not currently validate targets for governments or public sector institutions, government ownership does not necessarily mean that an entity is a public sector institution.
Depending on its portfolio, it could then be possible for the FI to set targets (e.g., engagement targets if the portfolio companies are not public sector institutions). On real estate, there is currently a call for companies and FIs to pilot test the Buildings Sector Guidance.
Improving data is encouraged and it is recommended to then review if targets need to be adjusted accordingly. The minimum requirement, however, would be for targets to be revalidated at least every five years.