How to gain skills in project management?
Time management: I recommend to everyone the book Getting things done by David Allen. It is briefly summarized in different YouTube videos and is about personal organization and stressfree productivity.

Project management: For project management and a good visualization of your process (e.g. of publishing a paper) you might want to look into IT Kanban and use a real Kanban board or a software like Trello. If you work in a team on that project, look into Scrum. Also, shared calendars are helpful (e.g. Google calendar).

People management: For teams, it could make sense to use a team collaboration tool like Slack (or Mattermost).