🪲 [Fix]: Module API and validation no longer include template leftovers (#17)

Domeneshop's public API and repository-local validation now exclude
template leftovers. The accidental greeting command is no longer
included, and checks that are now provided centrally are removed from
this repository.

## Fixed: Template command no longer appears in the public API

The module no longer exposes a generic greeting command left over from
its template. Domeneshop users now see only commands related to
authentication, domains, DNS, HTTP forwards, dynamic DNS, and invoices.

## Changed: Validation moved to shared pipeline

Repository-local copies of public-help-link, module-requirement, and
test-layout checks are removed so those checks run from the shared
Process-PSModule implementation instead of being duplicated here.

The remaining public command help links continue to use their canonical
`https://psmodule.io/Domeneshop/Functions/...` destinations. Validation
is supplied centrally by PSModule/Process-PSModule#420 at final commit
[`28647f438aab940fcc58851e38e3a4ee6ce9b9c3`](PSModule/Process-PSModule@28647f4).

> [!IMPORTANT]
> This pull request depends on PSModule/Process-PSModule#420 at
`28647f438aab940fcc58851e38e3a4ee6ce9b9c3` and must not merge until
Domeneshop consumes a Process-PSModule release containing that change,
so centralized validation is active.

---
<details>
<summary>Technical details</summary>

- Removes `src/functions/public/Get-PSModuleTest.ps1` and
`tests/Get-PSModuleTest.Tests.ps1`.
- Removes repository-local duplicates now centralized in shared tooling:
  - `tests/PublicHelpLinks.Tests.ps1`
  - `tests/ModuleRequirements.Tests.ps1`
  - `tests/TestLayout.Tests.ps1`
- Leaves canonical help links for remaining public commands unchanged.
- Exact upstream dependency: PSModule/Process-PSModule#420, final SHA
`28647f438aab940fcc58851e38e3a4ee6ce9b9c3`.
- Merge blocker: update Domeneshop to a Process-PSModule release that
contains that exact upstream change before merging this pull request.

</details>

<details>
<summary>Relevant issues (or links)</summary>

- PSModule/Process-PSModule#420

</details>

---------

Co-authored-by: Copilot App <223556219+Copilot@users.noreply.github.com>

Author: MariusStorhaug