"func-names" eslint rule fails when using private methods syntax

I have a code that uses private methods syntax in my index.js file:

class A {
  #field;

  constructor() {
    this.#field = 'foo';
  }

  publicMethod() {
    this.#privateMethod();
  }

  #privateMethod() {  // The problem string
    this.#field = 'bar';
  }
}

const a = new A();
a.publicMethod();

I also have "func-names" rule enabled in my .eslintrc.

The code itself works perfectly, but eslint check fails for some reason:

.../src/index.js
  12:17   error   Unexpected unnamed function   func-names

Is there any way to get eslint to process this case correctly?

The setup is:

package.json

  ...
  "devDependencies": {
    "@babel/core": "^7.12.3",
    "@babel/eslint-parser": "^7.12.1",
    "@babel/eslint-plugin": "^7.12.1",
    "@babel/plugin-proposal-class-properties": "^7.12.1",
    "@babel/plugin-proposal-private-methods": "^7.12.1",
    "@babel/preset-env": "^7.12.1",
    "babel-loader": "^8.1.0",
    "eslint": "^7.5.0",
    "webpack": "^5.2.0",
    "webpack-cli": "^4.1.0"
  },
  ...

.babelrc

{
  "presets": [
    ["@babel/preset-env", { "targets": { "esmodules": true } } ]
  ],
  "plugins": [
    ["@babel/plugin-proposal-class-properties", { "loose": true } ],
    ["@babel/plugin-proposal-private-methods", { "loose": true } ]
  ]
}

.eslintrc

{
  "rules": {
    "func-names": "error"
  },
  "parser": "@babel/eslint-parser",
  "plugins": [
    "@babel"
  ]
}