Check semver violations via CI

[orhun]

Is your feature request related to a problem? Please describe.

The last release of git-cliff-core had a breaking change:

error[E0063]: missing fields `field` and `pattern` in initializer of `CommitParser`
   --> crates/release_plz_core/src/changelog.rs:192:9
    |
192 |         CommitParser {
    |         ^^^^^^^^^^^^ missing `field` and `pattern`

And we don't have the processes set up to check these kind of situations during the development phase.

Describe the solution you'd like

Use cargo-semver-checks in CI via cargo-semver-checks-action.

Describe alternatives you've considered

Add cargo-semver-checks to the release script for checking the semver violations before the release.

Additional context

• https://discord.com/channels/1093977388892819553/1093977389672956026/1168300333273976863