interface MyExtensionInterface extends ExtensibleDataInterface
{
    const ENTITY_ID = "entity_id";
    const INVOICE_ID = "invoice_id";

    // Foreign key to the sales_invoice table
    public function getInvoiceId();
    public function setInvoiceId();

    public function getMyValue();
    public function setMyValue();

    public function getExtensionAttributes();
    public function setExtensionAttributes(MyCompanyMyExtensionAttributeApiDataMyExtensionInterface $extensionAttributes);
}

class MyProvider implements MyExtensionProviderInterface
{
    public function __construct
    (
        EntityManager $entityManager,
        Loader $loader,
        MyExtensionFactory $myExtensionFactory
    ) {
        $this->entityManager = $entityManager;
        $this->loader = $loader;
        $this->myExtensionFactory = $myExtensionFactory;
    }

    // This is the method where I want to update the extension attribute's
    // value, and then update it in the database
    public function setMyExtensionValue($invoiceId, $value)
    {
        $ids = $this->loader->getMyExtensionAttributeByInvoiceId($invoiceId);

        if (count($ids) > 0)
        {
            $id = $ids[0];
            $myExtension = $this->myExtensionFactory->create();
            $this->entityManager->load($myExtension, $id);
        }
        else
        {
            $myExtension = $this->myExtensionFactory->create();
            $myExtension->setInvoiceId($invoiceId);
        }

        $myExtension->setMyValue($value);

        // This is where I'm getting an unique constraint violation
        $this->entityManager->save($myExtension);
    }
}

class Loader
{
    private $metadataPool;
    private $resourceConnection;

    public function __construct
    (
        MagentoFrameworkEntityManagerMetadataPool $metadataPool,
        ResourceConnection $resourceConnection
    ) {
        $this->metadataPool = $metadataPool;
        $this->resourceConnection = $resourceConnection;
    }

    public function getMyExtensionAttributeByInvoiceId($invoiceId)
    {
        $metadata = $this->metadataPool->getMetadata(MyExtensionInterface::class);
        $connection = $this->resourceConnection->getConnection();
        $select = $connection
            ->select()
            ->from($metadata->getEntityTable(), MyExtensionInterface::ENTITY_ID)
            ->where(MyExtensionInterface::INVOICE_ID . ' = ?', $invoiceId);
        $ids = $connection->fetchCol($select);
        return $ids ?: [];
    }
}