I want to be included in more projects and meetings at work, how do you recommend I go about asking to be included?

Hi there! First, what is holding you back? (e.g. a trust issue with a manager; your newness in the role; a lack of understanding around the company culture/expectations; personal fears and insecurities) The answer will vary in each of those scenarios, but the one thing that fits all I'd want to know is have you ASKED? If so, what was the reaction? If you haven't, well now is the time.
If it's about speaking up in meetings, you may not even have to ask, you may be expected to just contribute if you have something to say. So give that a try.
If it's about being simply invited, try a convo with your manager about bringing you to meetings where your work is involved. This might be more beneficial for everyone. Remember how Katherine in "Hidden Figures" was able to solve problems more effectively when she had context from attending meetings? Maybe you can make that case!
As it relates to more leadership on projects, chat with your boss and team about your skills and expertise and how you can best contribute when you are included more!
I encourage you to boil down to what is preventing you from participating fully, because your voice needs to be heard at work. Your coworkers need to see you as a potential leader and know the value you bring. They can't do that if you aren't stepping up and speaking up!!! (Coach A)