I would not consider project planning to be an umbrella activity, but it is most certainly an SDLC activity.
There are lots of different ways to slice the SDLC into phases and then organize those phases into different types of lifecycle models, ranging from the purely sequential to highly iterative and incremental models. However, they all tend to have similar activities - initiation, ideation and concepting, planning, requirements development, design, development, integration, implementation, operations, and disposition.
Project planning is a subset of the activities in project management. Other project management activities include project initiation, estimation (of cost and/or time), resource allocation, risk management, supplier management, measurement, monitoring and control, and project closeout.
Project management, as a whole, is an umbrella activity that extends across the entire project life. However, not all of the activities within project management are umbrella activities. Some may recur at different points, but recurrence (even regularly or on a cadence) does not make the activity an umbrella activity.
Project planning is typically done once. Even in iterative methodologies, you tend to plan an increment (for example, a Sprint in Scrum). You then have milestones or events at which you can review your work against plan and make changes. Changes are not always required, though.
Of the project management activities that I've identified, I would consider risk management, measurement, and monitoring and control to be umbrella activities. However, depending on what you find when performing these, you may trigger an occurrence of a different project management activity, such as project planning to replan your project or resource allocation to adjust the people and resources available to the project.