feat: add biome to registry (#4283)

Add [biome](https://github.com/biomejs/biome) to registry using aqua and
ubi backends.

docs/registry.md

@@ -87,6 +87,7 @@ You can also specify the full name for a tool using `mise use aqua:1password/cli
 | benthos | [aqua:benthosdev/benthos](https://github.com/benthosdev/benthos) [asdf:benthosdev/benthos-asdf](https://github.com/benthosdev/benthos-asdf) |
 | bfs | [asdf:mise-plugins/mise-bfs](https://github.com/mise-plugins/mise-bfs) |
 | binnacle | [aqua:Traackr/binnacle](https://github.com/Traackr/binnacle) [asdf:Traackr/asdf-binnacle](https://github.com/Traackr/asdf-binnacle) |
+| biome | [aqua:biomejs/biome](https://github.com/biomejs/biome) [ubi:biomejs/biome](https://github.com/biomejs/biome) |
 | bitwarden | [aqua:bitwarden/clients](https://github.com/bitwarden/clients) [asdf:vixus0/asdf-bitwarden](https://github.com/vixus0/asdf-bitwarden) |
 | bitwarden-secrets-manager | [ubi:bitwarden/sdk](https://github.com/bitwarden/sdk) [asdf:asdf-community/asdf-bitwarden-secrets-manager](https://github.com/asdf-community/asdf-bitwarden-secrets-manager) |
 | black | [aqua:psf/black](https://github.com/psf/black) |

registry.toml

@@ -195,6 +195,8 @@ bbr-s3-config-validator.backends = ["asdf:mise-plugins/tanzu-plug-in-for-asdf"]
 benthos.backends = ["aqua:benthosdev/benthos", "asdf:benthosdev/benthos-asdf"]
 bfs.backends = ["asdf:mise-plugins/mise-bfs"]
 binnacle.backends = ["aqua:Traackr/binnacle", "asdf:Traackr/asdf-binnacle"]
+biome.backends = ["aqua:biomejs/biome", "ubi:biomejs/biome"]
+biome.test = ["biome --version", "Version: {{version}}"]
 bitwarden.backends = ["aqua:bitwarden/clients", "asdf:vixus0/asdf-bitwarden"]
 bitwarden.test = [
     "bw --version",