fix: align biome init and formatter ownership

[zeitlinger]

Summary

• generate biome.json with explicit space indentation during flint init
• keep Prettier full-mode scoped to its declared Markdown/YAML patterns
• add an e2e regression for the biome.jsonc formatter ownership conflict

Testing

• cargo test fix_exits_nonzero_when_formatters_disagree_on_same_file --test e2e -- --nocapture
• FLINT_CASES=prettier cargo test cases

[Copilot]

Pull request overview

This PR adjusts formatter “ownership” so Biome and Prettier don’t both try to format the same files, while also ensuring flint init generates a Biome config that matches the repo’s space-indentation style.

Changes:

• Generate a biome.json with explicit 2-space indentation during flint init when Biome is selected and no Biome config exists.
• Remove Prettier’s project-wide --full command so full-mode remains scoped to its declared *.md/*.yml/*.yaml patterns.
• Add an e2e regression test covering the Prettier-vs-Biome formatter ownership conflict on biome.jsonc.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
tests/e2e.rs	Adds an e2e regression ensuring --full Prettier doesn’t target Biome-owned JSONC and that fix exits non-zero on disagreement.
tests/cases/general/init-rust/test.toml	Updates the init snapshot to expect biome.json generation and its contents.
src/registry/checks.rs	Removes Prettier’s full_cmd so full-mode doesn’t run against {ROOT}.
src/init/mod.rs	Detects Biome selection and triggers Biome config generation; adds unit tests for the new generator.
src/init/generation.rs	Implements generate_biome_config() to write biome.json with explicit space indentation.

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