Looking at the issues on github, it seems it might, but I couldn't find a specific statement in the docs that Vue 2.. is strictly semver, and therefore offer full backward compatibility. Have I missed it or is not stated anywhere ?
No, I don't believe we do state it, but Vue does try to follow semver in all its projects - at least for documented features and behavior. For undocumented behavior or exposed internals, we describe changes in release notes.
What would you think about a note on the installation page?
I just need to know if its semver before updating to a new version. I dont mind where its stated, but it should be stated somewere.
Maybe add labels for new api properties. Small green image with text about version. And show this label in navigation menu.

I like that idea too. Will try to add it this week, but a PR is also welcome if someone wants to jump on it immediately. We note when items were introduced in the guide.
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I just need to know if its semver before updating to a new version. I dont mind where its stated, but it should be stated somewere.