Tell your boss.
You do good work for a reasonable wage. You have improved over time, and have executed well in several different roles.
As someone who has employed a lot of people in my life, you are my dream employee so far!
If you came to me and said you were looking for more challenge, more growth, more something, I would have a very good idea of what you are good at, and the kind of thing that could make you really a strong performer at this company.
And that's my job, as a manager. Happy employees who enjoy their work are the kinds of people that other people want to work with. So if I make you happy, and you produce even better work, not just you and I win... the whole company does.
Listen. Your boss has a LOT more experience in the industry than you do. They know if jobs and roles that you have never heard of before. You are 28. Talk to your boss and tell them you want to grow in the company, but you aren't sure what to target / what to learn / who to talk to / what fits your personality and skills.
And you and your boss's relationship will be even better for it.
Note: A headhunter doesn't care about you. You don't make enough money, and you have no power or influence or network. So you are basically useless to a headhunter, who works with people who CHANGE the companies they go to. Because headhunters get a finders fee between 50% and 100% of your annual salary. That means that they need to find someone who thinks you are so valuable that the company is going to pay DOUBLE your salary just to hire you. And honestly, at this point in your career, you just don't have that kind of value to anyone. Sorry. It's just numbers.