[eslint-config] Support for Biome.js

[yumin-chen]

Summary

@rushstack+eslint-patch doesn't support Biome.js

    Error: Failed to patch ESLint because the calling module was not recognized.
    If you are using a newer ESLint version that may be unsupported, please create a GitHub issue:
    https://github.com/microsoft/rushstack/issues

Repro steps

Run npx @biomejs/biome migrate eslint --write to migrate from an existing ESLint project that uses eslint-config-next.

Expected result: Successfully patch the ESLint config.

Actual result:

  ✖ Migration has encountered an error: `node` was invoked to resolve '/Users/yuminch/Workspace/sveltia-next-ts/node_modules/.pnpm/eslint-config-next@14.2.28_eslint@8.57.1_typescript@5.8.3/node_modules/eslint-config-next/index.js'. This invocation failed with the following error:
    /Users/yuminch/Workspace/sveltia-next-ts/node_modules/.pnpm/@rushstack+eslint-patch@1.11.0/node_modules/@rushstack/eslint-patch/lib/_patch-base.js:167
                throw new Error('Failed to patch ESLint because the calling module was not recognized.\n' +
                      ^

    Error: Failed to patch ESLint because the calling module was not recognized.
    If you are using a newer ESLint version that may be unsupported, please create a GitHub issue:
    https://github.com/microsoft/rushstack/issues
        at Object.<anonymous> (/Users/yuminch/Workspace/sveltia-next-ts/node_modules/.pnpm/@rushstack+eslint-patch@1.11.0/node_modules/@rushstack/eslint-patch/lib/_patch-base.js:167:19)
        at Module._compile (node:internal/modules/cjs/loader:1275:14)
        at Module._extensions..js (node:internal/modules/cjs/loader:1329:10)
        at Module.load (node:internal/modules/cjs/loader:1133:32)
        at Module._load (node:internal/modules/cjs/loader:972:12)
        at Module.require (node:internal/modules/cjs/loader:1157:19)
        at require (node:internal/modules/helpers:119:18)
        at Object.<anonymous> (/Users/yuminch/Workspace/sveltia-next-ts/node_modules/.pnpm/@rushstack+eslint-patch@1.11.0/node_modules/@rushstack/eslint-patch/lib/modern-module-resolution.js:11:23)
        at Module._compile (node:internal/modules/cjs/loader:1275:14)
        at Module._extensions..js (node:internal/modules/cjs/loader:1329:10)

    Node.js v19.9.0

Details

Standard questions

Please answer these questions to help us investigate your issue more quickly:

Question	Answer
@rushstack/eslint-config version?
Operating system?
Would you consider contributing a PR?
TypeScript compiler version?
Node.js version (node -v)?

[iclanton]

Can you provide a repro repo?