Add API stability checks to the library

[V0ldek]

Is your feature request related to a problem? Please describe.
Breaking changes should be controlled. While we're not at v1.0.0 yet, we try to record all breaking changes in releases. Tracking those is rather hard without automated tools.

Describe the solution you'd like
Investigate and use the available tools. The ones I'm aware of are:

• cargo-semver-checks
• cargo-public-api

First investigate and choose one to be callable locally with just. Adding it to CI is another PR.

[github-actions]

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