We start with the State Council directives
Both those documents were issued by the State Council rather than by SASAC. This makes a difference. The State Council has supervision over all of the state-owned enterprises, whereas SASAC has a dual role. It issues regulations on the disposition of state property, but also has shareholder power over industries which are controlled by the central government.
What I think happened was that the section three of State Council opinion called for the relevant authorities to list strategic industries under their jurisdiction, and SASAC informally mentioned which central SOE’s it would list as strategic industries.
The seven industries then wouldn’t be a comprehensive list of strategic industries, merely the industries under direct SASAC control that they plan to list.
Finance isn’t listed because it isn’t under the direct jurisdiction of SASAC. The big four banks are owned by Central Huijin which is run by the Ministry of Finance, and the other banks are owned by local governments. Also finance doesn’t meet the criteria mentioned by the State Council, and in any case the CBRC is not about to cede regulatory authority to SASAC.