Any strategic or tactical advice is particular to each company. This is not a skill. The other skills include mentoring, so this seems a little redundant.
It's different from mentoring. It's being good at making sure management is aware of your coworker's accomplishments. It's a managing up skill instead of managing down skill.
For example, when you as a senior engineer are in a meeting with management and without the junior engineers, it's important to call out "Jr. Eng X did this part of the project and did a great job".
Yeah, a lot of this is providing visibility to low visibility high impact work or Anchoring[1] work so people's impact is correctly reflected as a part of whatever review process an organization does.
> How to help someone get promoted
Any strategic or tactical advice is particular to each company. This is not a skill. The other skills include mentoring, so this seems a little redundant.