Hetzner cloud provider incorrectly inherited in modules

I’m learning Terraform and trying to organize the code in modules. The code uses two providers, aws and hetznercloud/hcloud. The first one works alright, but the hcloud declaration is not inherited in the module. This is how they are declared in main.tf:

provider "hcloud" {
  token = var.hcloud_token
provider "aws" {
  region = "eu-west-2"

When I run terraform init, though, Terraform tries to use hashicorp/hcloud instead of hetznercloud/hcloud and fails:

Initializing provider plugins...
- Finding latest version of hashicorp/hcloud...
- Reusing previous version of hetznercloud/hcloud from the dependency lock file
- Reusing previous version of hashicorp/aws from the dependency lock file
- Using previously-installed hetznercloud/hcloud v1.26.2
- Using previously-installed hashicorp/aws v3.45.0
│ Error: Failed to query available provider packages
│ Could not retrieve the list of available versions for provider hashicorp/hcloud: provider registry registry.terraform.io does not have a provider named
│ registry.terraform.io/hashicorp/hcloud
│ Did you intend to use hetznercloud/hcloud? If so, you must specify that source address in each module which requires that provider. To see which modules
│ are currently depending on hashicorp/hcloud, run the following command:
│     terraform providers

Here’s the output of terraform providers:

Providers required by configuration:
├── provider[registry.terraform.io/hetznercloud/hcloud]
├── provider[registry.terraform.io/hashicorp/aws]
└── module.mod_zookeeper
    ├── provider[registry.terraform.io/hashicorp/hcloud]
    └── provider[registry.terraform.io/hashicorp/aws]

I tried to redefine the providers in the module code, but then I get this message:

│ Error: Module module.mod_zookeeper contains provider configuration
│ Providers cannot be configured within modules using count, for_each or depends_on.

If I remove resources using Hetzner cloud from the module, the remaining aws providers works alright.
What’s wrong with hcloud?