`require.resolve` regression starts from Node v12 with `paths`

Version

v20.19.2

Platform

Darwin MacBookPro 24.5.0 Darwin Kernel Version 24.5.0: Tue Apr 22 19:54:49 PDT 2025; root:xnu-11417.121.6~2/RELEASE_ARM64_T6000 arm64

Subsystem

No response

What steps will reproduce the bug?

https://github.com/JounQin/test/tree/repro/node_require_resolve_paths

Simply run node test.js

On node 10:

`resolve` npm package: <CWD>/fixtures/bar.js
`require.resolve` built-in function: <CWD>/fixtures/bar.js

How often does it reproduce? Is there a required condition?

Persist

What is the expected behavior? Why is that the expected behavior?

There is a related old issue #29139.

What do you see instead?

On node 12+, of course including Node LTS (20+)

`resolve` npm package: /Users/JounQin/Workspaces/GitHub/test/fixtures/bar.js
node:internal/modules/cjs/loader:1404
  throw err;
  ^

Error: Cannot find module 'bar'
Require stack:
- <CWD>/test.js
    at Function._resolveFilename (node:internal/modules/cjs/loader:1401:15)
    at Function.resolve (node:internal/modules/helpers:145:19)
    at Object.<anonymous> (/Users/JounQin/Workspaces/GitHub/test/test.js:16:11)
    at Module._compile (node:internal/modules/cjs/loader:1730:14)
    at Object..js (node:internal/modules/cjs/loader:1895:10)
    at Module.load (node:internal/modules/cjs/loader:1465:32)
    at Function._load (node:internal/modules/cjs/loader:1282:12)
    at TracingChannel.traceSync (node:diagnostics_channel:322:14)
    at wrapModuleLoad (node:internal/modules/cjs/loader:235:24)
    at Function.executeUserEntryPoint [as runMain] (node:internal/modules/run_main:171:5) {
  code: 'MODULE_NOT_FOUND',
  requireStack: [ '<CWD>/test.js' ]
}

Additional information

I believe there is no reports because most projects use http://npmjs.com/resolve instead, and it behaviors same as Node 10-, and I'm trying to remove resolve as dependency, so I just met this issue at https://github.com/un-ts/eslint-plugin-import-x/pull/272#issuecomment-2915145320

cc @cjihrig

Run the linked reproduction's test.js under Node 10 and Node 12+ and compare the require.resolve results when paths is supplied. Read the CommonJS loader path shown in the stack trace and related issue #29139; done means the reproduction resolves fixtures/bar.js consistently without the external resolve package.