add a new extension attribute to the order:
<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Api/etc/extension_attributes.xsd">
<extension_attributes for="Magento\Sales\Api\Data\OrderInterface">
<attribute code="payment_method" type="string" >
<join reference_table="sales_order_payment" reference_field="parent_id" join_on_field="entity_id">
<field>method</field>
</join>
</attribute>
</extension_attributes>
</config>
then use OrderRepository as per your requirement:
$filter = $this->filterBuilder->setField('extension_attribute_payment_method.method')
->setConditionType('eq')
->setValue($methodCode)
->create();
$searchCriteria = $this->searchCriteriaBuilder
->addFilters([$filter])
->create();
$orderList = $this->orderRepository->getList($searchCriteria);
$numberOrders = $orderList->getTotalCount();
$result = $orderList->getItems();