Using npm link with a module utilizing Nuxt3 ends in error

Question

I want to create an npm module with Nuxt 3 components. For that I defined the "nuxt.js" file the following way.

import { join } from 'path'
import { defineNuxtModule} from '@nuxt/kit'

export default defineNuxtModule({
    hooks: {
        'components:dirs'(dirs){
            dirs.push({
                path: join(__dirname, 'components'),
                prefix: 'my-name'
            })
        }
    }
})

When I publish the module and then run npm install my-module, there is no problem. I can utilize the Nuxt 3 components. However, since I want to also test if everything works as intended, I want to use npm link to test the module without publishing it.

So I execute "npm link" and then "npm link 'my-module'" in both directories. The module gets linked correctly and I can find it in my "node-modules" directory. But when running "npm run dev" I get the following error:

 ERROR  Cannot start nuxt:  Cannot find module '@nuxt/kit'                                                                                                                          07:39:52
Require stack:
- /path/my-module/nuxt.js

  Require stack:
  - /path/my-module/nuxt.js
  at Function.Module._resolveFilename (internal/modules/cjs/loader.js:902:15)
  at Function.resolve (internal/modules/cjs/helpers.js:107:19)
  at _resolve (node_modules/jiti/dist/jiti.js:1:108226)
  at jiti (node_modules/jiti/dist/jiti.js:1:110413)
  at /path/my-module/nuxt.js:2:12
  at jiti (node_modules/jiti/dist/jiti.js:1:112282)
  at requireModule (node_modules/@nuxt/kit/dist/index.mjs:295:26)
  at normalizeModule (node_modules/@nuxt/kit/dist/index.mjs:448:53)
  at installModule (node_modules/@nuxt/kit/dist/index.mjs:431:47)
  at initNuxt (node_modules/nuxt/dist/index.mjs:1389:13)

When I try to run "npm install @nuxt/kit" it just removes "my-module" from the node-modules folder. When I then relink it, I run into the same error.

I want to test the module locally. Is there a way to fix that, and if not, is there another way to do that? (yarn link runs into the same problem)