I'm thinking about switching careers but I don't know where to start or who to talk to. Should I reach out to my mentor or a career coach?

Yay!! I'm glad you have a mentor. That's a good start. So is a career coach! Before you even go there though, do you have clarity on what you want to switch to (and why)? The grass isn't always greener and there are real hardships even when you are in your dream job. make sure you are clear on what is motivating the switch.
Then, DO YOUR RESEARCH. That includes googling that potential career path, looking on LinkedIn to see who you are connected to that has your dream new role and reading their profiles to get an idea of their experiences, as well as asking them for informational interviews.
Is the switch you are looking to make common? Will you need new need credentials or training? What transferable skills have you gathered in your current field that you can take to your next role?
Collect all the info that you can and then work with both your mentor and coach to strategize for how you will make this switch as seamlessly as possible.