Magento 2 | Join a table to getLoadedProductCollection()

I’m trying to join the tier price table to the getLoadedProductCollection () collection located in the list.phtml file.

What I would like to do is filter the products in the current category by tier price like so:

$joinConditions = 'e.entity_id = tier.entity_id';
    $_productCollection = $block->getLoadedProductCollection();
    $_productCollection->getSelect()->join(
             'catalog_product_entity_tier_price as tier',
             $joinConditions
            )->where('tier.all_groups = 0')
              ->where('tier.customer_group_id = 0')
              ->where('tier.qty <= 1000')
              ->where('tier.value <= 0.70')
              ->where('tier.website_id = 0');

The following code does not generate an error but does not apply any filters and I keep seeing the same products over and over.

Where is the mistake?