How to apply discount after tax programatically for a Magento 2 order?

For Tax configuration, there are two ways to fix this.
In backend configuration:
Apply Customer Tax ->set ‘Before Discount’; This should fix your problem I guess.

You can customize the code as well for same :
In your di.xml, add as below:

<preference for="MagentoTaxModelSalesTotalQuoteTax" type="<yournamespace><yourModule>ModelSalesTotalQuoteTax"/>

Now create your class file Tax.php and add below code:

namespace <yournamespace><yourModule>ModelSalesTotalQuote;

class Tax extends MagentoTaxModelSalesTotalQuoteTax

{
    /* override code here */
    public function __construct(
        /* add dependency classes here */    ) {
        parent::__construct(
            /* parent class objects here */
        );
    }

    /**
    * Custom Collect tax totals for quote address
    *
    * @param Quote $quote
    * @param ShippingAssignmentInterface $shippingAssignment
    * @param AddressTotal $total
    * @return $this
    */
    public function collect(
        MagentoQuoteModelQuote $quote,
        MagentoQuoteApiDataShippingAssignmentInterface $shippingAssignment,
        MagentoQuoteModelQuoteAddressTotal $total
    ) {

       /* your calculation here goes here */
        $total->setTaxAmount($set_your_tax_here);

        return $this;
    }

}

Hope this helps!