Will Macbook Air 2017 benefit from Catalina upgrade?
However, is it worth actually upgrading?

A newer macOS release always includes the latest security patches for any discovered hardware of software vulnerabilities. So generally speaking, it's a good idea to upgrade if your device supports running it, given you have no reason to refrain from upgrading.

I know I can't use certain features (such as the battery health or sidecar), but should I do it for security, etc?

Yes.

What are the experiences of other MBA 2017 owners after upgrade? Has anyone experienced slowdowns? Is anything actually better? Or should I just stick with Good Ol' Mojave?

This experience could be pretty subjective depending on the apps being used, but generally speaking, a newer release of macOS also often includes under the hood performance improvements which are also claimed about by Apple.