I hear a lot about people considering themselves "solo" developers but I have the impression that everyone has a slightly different definition for what that is. What do you think?

Being solo is:

• Making everything including engine?
• Making everything but not necessarily engine?
• Designing the game and core aspects while at time hiring freelancers (but still doing most of the things yourself)?
• Running a 'game studio' by yourself eventually hiring people to do small tasks (not design but for example music)?
• Assembling everything by yourself but buying and effectivelly using bought assets for some parts?

The bullet points could be levels of 'solo'. For example: I am solo, however, I use others engines and such because I am 'not there' yet.

I don't think using third-party assets, tools, and code makes you any less of a solo developer. The key distinction is, are the people who make these third-party assets working specifically on your game, or are they simply providing a product that you happened to buy?

If your game displays any text in a font you didn't create yourself, you are using third-party assets. If you call any function from the standard library of your chosen programming languages, you use third-party code. And absolutely everybody uses third-party tools.

Freelancers are more of a borderline case. And if you have actual employees, you should treat them as part of the team, no matter how small their contributions.