Type errors while using @octokit/plugin-throttling with getOctokit

[pose]

(Potentially related to actions/github-script#229, but I don't think it's a duplicate)

Describe the bug
I am facing GitHub rate limiting issues so I want to throttle my requests. However, when I add @octokit/plugin-throttling to the call of github.getOctokit, I am getting a TypeScript compile error I cannot get rid of.

To Reproduce

(Note: you can see this issue affecting following PR: aws-actions/stale-issue-cleanup#392)

Steps to reproduce the behavior:

1. Pre-reqs

This is my package.json:

{
  "name": "stale-issue-cleanup",
  "version": "7.1.0",
  "description": "GitHub Action that cleans up old and response-reqested issues",
  "private": true,
  "main": "src/entrypoint.ts",
  "scripts": {
    "check-lint": "prettier --list-different src/**.js && eslint src/**.js",
    "lint": "biome check --write src",
    "test": "npm run lint && vitest run && npm run build",
    "build": "tsc",
    "package": "npm run build && ncc build -s -m --license THIRD-PARTY -o dist && node -e \"require('fs').cpSync('dist/THIRD-PARTY', './THIRD-PARTY')\"",
    "coverage": "vitest run --coverage"
  },
  "engines": {
    "node": ">=18"
  },
  "repository": {
    "type": "git",
    "url": "git+https://github.com/aws-actions/stale-issue-cleanup"
  },
  "license": "Apache-2.0",
  "bugs": {
    "url": "https://github.com/aws-actions/stale-issue-cleanup/issues"
  },
  "homepage": "https://github.com/aws-actions/stale-issue-cleanup/#readme",
  "dependencies": {
    "@actions/core": "^1.11.1",
    "@actions/github": "^6.0.1",
    "@octokit/core": "^7.0.6",
    "@octokit/plugin-throttling": "^11.0.3",
    "dateformat": "^4.4.1"
  },
  "devDependencies": {
    "@biomejs/biome": "2.1.2",
    "@fetch-mock/vitest": "^0.2.14",
    "@octokit/plugin-rest-endpoint-methods": "^13.3.0",
    "@types/dateformat": "^5.0.3",
    "@types/node": "^24.1.0",
    "@vercel/ncc": "^0.38.3",
    "@vitest/coverage-v8": "^2.1.8",
    "dotenv": "^17.2.1",
    "typescript": "^5.8.3",
    "vitest": "^2.1.8"
  }
}

This is my tsconfig.json:

{
  "compilerOptions": {
    "target": "ES2022",
    "module": "commonjs",
    "declaration": true,
    "outDir": "dist",
    "declarationDir": "dist/types",
    "sourceMap": true,
    "strict": true,
    "noImplicitAny": true,
    "strictNullChecks": true,
    "noImplicitThis": true,
    "alwaysStrict": true,
    "noUnusedLocals": true,
    "noUnusedParameters": true,
    "noImplicitReturns": true,
    "noFallthroughCasesInSwitch": true,
    "experimentalDecorators": true,
    "strictPropertyInitialization": true,
    "esModuleInterop": true,
  },
  "exclude": ["node_modules", "dist", "test", "vitest.config.ts"]
}

2. This is the code I am trying to write

    import * as github from '@actions/github';
    // ...

    const client = github.getOctokit(args.repoToken, {
      request: { fetch: fetchImpl || globalThis.fetch },
      throttle: {
        onRateLimit: (retryAfter: number, options: EndpointDefaults, octokit: Octokit, retryCount: number) => {
          octokit.log.warn(
            `Request quota exhausted for request ${options.method} ${options.url}. Retrying after ${retryAfter} seconds!`,
          );
    
          if (retryCount < 3) {
            // only retries 3 times
            octokit.log.info(`Retrying after ${retryAfter} seconds! ${retryCount} times`);
            return true;
          }
          return undefined;
        },
        onSecondaryRateLimit: (retryAfter: number, options: EndpointDefaults, octokit: Octokit) => {
          // does not retry, only logs a warning
          octokit.log.warn(
            `SecondaryRateLimit detected for request ${options.method} ${options.url}. Retrying after ${retryAfter} seconds!`,
          );
          return undefined;
        },
      },
    }, throttling);
    ...

3. Error

This is the type error I'm getting on the last line of the snippet above:

Argument of type 'typeof throttling' is not assignable to parameter of type 'OctokitPlugin'.
  Types of parameters 'octokit' and 'octokit' are incompatible.
    Type 'import("/workspace/stale-issue-cleanup/node_modules/@actions/github/node_modules/@octokit/core/dist-types/index").Octokit' is not assignable to type 'import("/workspace/stale-issue-cleanup/node_modules/@octokit/core/dist-types/index").Octokit'.
      The types returned by 'request.defaults(...)(...)' are incompatible between these types.
        Type 'Promise<import("/workspace/stale-issue-cleanup/node_modules/@octokit/types/dist-types/OctokitResponse").OctokitResponse<any, number>>' is not assignable to type 'Promise<import("/workspace/stale-issue-cleanup/node_modules/@octokit/request/node_modules/@octokit/types/dist-types/OctokitResponse").OctokitResponse<any, number>>'.
          Property 'retryCount' is missing in type 'import("/workspace/stale-issue-cleanup/node_modules/@octokit/types/dist-types/OctokitResponse").OctokitResponse<any, number>' but required in type 'import("/workspace/stale-issue-cleanup/node_modules/@octokit/request/node_modules/@octokit/types/dist-types/OctokitResponse").OctokitResponse<any, number>'.ts(2345)
index.d.ts(15, 9): 'retryCount' is declared here.

Expected behavior

No TypeScript errors are reported and project compiles fine.