How to get current Website ID in the Admin Panel?

The general idea is to pass the scope, chosen, through the request parameter.

I think you should use the similar code like in the product edit action:

/** @var \Magento\Store\Model\StoreManagerInterface $storeManager */
$storeManager = $this->_objectManager->get('Magento\Store\Model\StoreManagerInterface');
$storeId = (int) $this->getRequest()->getParam('store', 0);
$store = $storeManager->getStore($storeId);
$storeManager->setCurrentStore($store->getCode());

In this case $store->getWebsiteId() should be actual (selected) website id. But this can be done only in case you use the store block which works in the same way as a standard magento block (to select a store scope):

Here is my result in the example when I select the default store view (id == 1):

and here is for the default global scope (All Store Views, website id is 0):

---

Update:

You can add a method like this in the helper and use it where you want:

/**
 * @var \Magento\Framework\App\State
 */
protected $state;

/**
 * @var \Magento\Store\Model\StoreManagerInterface
 */
protected $storeManager;

/**
 * Data constructor.
 * @param Context $context
 * @param \Magento\Framework\App\State $state
 * @param \Magento\Store\Model\StoreManagerInterface $storeManager
 */
public function __construct(
    Context $context,
    \Magento\Framework\App\State $state,
    \Magento\Store\Model\StoreManagerInterface $storeManager
) {
    parent::__construct($context);
    $this->state = $state;
    $this->storeManager = $storeManager;
}

/**
 * @return int
 */
public function resolveCurrentWebsiteId()
{
    if ($this->state->getAreaCode() == \Magento\Framework\App\Area::AREA_ADMINHTML) {
        // in admin area
        /** @var \Magento\Framework\App\RequestInterface $request */
        $request = $this->_request;
        $storeId = (int) $request->getParam('store', 0);
    } else {
        // frontend area
        $storeId = true; // get current store from the store resolver
    }

    $store = $this->storeManager->getStore($storeId);
    $websiteId = $store->getWebsiteId();

    return $websiteId;
}

Result should be like this:

1. Backend without scope selector - 0

   

2. Backed with scope selector - selected website id or 0 if nothing selected (All Store Views)

   

3. Frontend - current website id

   

---

If you are looking for the short-way on the frontend:

You can use the Magento\Store\Model\StoreResolver class for that purpose:

/**
 * @var \Magento\Store\Model\StoreResolver
 */
private $storeResolver;

/**
 * @param \Magento\Store\Model\StoreResolver $storeResolver
 */
public function __construct(
    \Magento\Store\Model\StoreResolver $storeResolver
) {
    $this->storeResolver = $storeResolver;
}

/**
 * Returns the current store id, if it can be detected or default store id
 * 
 * @return int|string
 */
public function getCurrentStoreId()
{
    return $this->storeResolver->getCurrentStoreId();
}

It is correctly detects the currently selected store view on the frontend area, but useless for the admin area.