Nested npm projects select wrong tools with flycheck and lsp

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- [X] The issue can be reproduced on the **latest** available commit of Doom.

- [X] The issue can be reproduced on a stable release of Emacs, such as 27, 28, or 29. *(Unstable versions end in .50, .60, or .9x)*

### Expected behavior

I primarily work on a project with nested npm packages.

When opening a file that is inside a subpackage, flycheck should find `eslint` in the `node_modules` directory of the subpackage ie. `/package-a/node_modules/.bin/eslint`.

### Current behavior

Currently, flycheck uses `eslint` from the root directory.

This is because the function `+javascript-add-npm-path-h` uses projectile to find the root dir and adds `node_modules/bin` to the path.

### Steps to reproduce

# Package Structure
1. Create project :: `mkdir bug-repro`
2. Initialize npm :: `npm init -y`
3. install eslint :: `npm i eslint`
4. Create an eslint config :: `echo '{"rules": { "no-unused-vars": "error"}}` > .eslintrc`
5. Create a file w/ violation :: `echo 'const x = 10;' > index.js`
6. Create subpackage :: `mkdir subpackage`
7. `cd subpackage`
8. Initialize new npm project :: `npm init -y`
9. Install eslint :: `npm i eslint`
10. Create slightly different eslint config :: `echo '{"rules": { "no-unused-vars": "warn"}}` > .eslintrc`
11. Create a file w/ violation :: `echo 'const x = 10' > index.js`

# Checking
use `flycheck-verify-setup` to see that in both cases the eslint binary is the binary from the root.

### System Information

https://gist.github.com/bolivier/af0ab99120f44c4d52a85f2330de7c45