Should a smartwatch track the user's emotions?

No, I wouldn't want any of that. It's too personal. Especially wouldn't want it fed to some AI thing that I don't personally control.

My Samsung watch has something to measure stress, but it does it automatically and seems to think I'm stressed all the time (but maybe it's right lol)

I don't think users are going to want to input that directly, but if it inferred it somehow that would be neat. Of course there's also the issue of data privacy, but I'm sure you're aware of that.

Yes, if I can use the smartwatch with free software, i.e., be sure that this data will not be misused.

What does the software being free or paid have to do with the data being or not being misused?

Free software as in freedom, not price. Free software allows to verify what the device does and control it by modifying the code. This is the basics of the 4 freedoms, https://www.gnu.org/philosophy/free-software-even-more-impor....

Hard no!