Magento 2: How to Filter a Product Collection By Store ID

You can do this with the method addStoreFilter(), see Magento\Catalog\Model\ResourceModel\Product\Collection#addStoreFilter()

the addStoreFilter() function will accept store ID or Store object as a parameter.

EG, to get all products for the current store:

public function getProducts(){
    return $this->collection->addStoreFilter($this->_storeManager->getStore()); 
}

Hopefully, this helps.

For now this looks like a bug, because there is no possibility to apply store filter with the ProductRepository::getList() method, passing store id as a filter of SearchCriteria.

In the getList implementation, you can find that all the filters from SearchCriteria applied to collection

    foreach ($searchCriteria->getFilterGroups() as $group) {
        $this->addFilterGroupToCollection($group, $collection);
    }

In Magento\Catalog\Model\ProductRepository::addFilterGroupToCollection there is special handling for Category filter, but there is no one for Store.

So, additional condition should be added to Magento\Catalog\Model\ProductRepository::addFilterGroupToCollection which checks whether we have store filter and if we have - set store id for collection, something like:

        if ($filter->getField() == \Magento\Catalog\Model\Product::STORE_ID) {
            $collection->setStore($filter->getValue());
            continue;
        }

Created internal bug for this issue, its number is MAGETWO-45950