Draft: Fix CI on trigger

Summary

1. Revert "ci: run tests on trigger"

This reverts commit d1043f4a (!349 (merged))

2. ci: rename variables for clarity

• VANILLA_DOCKER_IMAGE -> BASE_IMAGE_VANILLA
• PICODATA_DOCKER_IMAGE -> BASE_IMAGE_FORK
• test-picodata -> test-fork

3. ci: split build-base-image job on two

Also specify whether to push build-base image explicitly

4. ci: run tests on trigger

Ensure that

• New code is covered by tests
• API is documented
• Changelog is up to date
• Version is bumped in the appropriate Cargo.toml files