Update quote totals based on the VAT rate

In the checkout in the country_id dropdown I have 2 countries: FR and BE.
For FR I have a VAT percentage of 20% and for BE I have 21%.
My goal is to update the tax amount in the checkout.

When I switch countries I triggered an ajax request:

        $quote = $this->checkoutSession->getQuote();

        $quote->getShippingAddress()->setCountryId($countryId);
        if ($countryId === 'BE') {
            foreach ($quote->getAllItems() as $item) {
                   // do smth 
            }
        }
        $quote->collectTotals()->save();

I also made this observer, listening to this event: sales_quote_collect_totals_before :

public function execute(Observer $observer)
{
    $quote = $observer->getQuote();
    $countryId = $quote->getShippingAddress()->getCountryId();
    if ((string)$countryId === 'BE'){
        foreach ($quote->getAllItems() as $item) {
            $product = $item->getProduct();
            $product->setTaxClassId(14);  //14 is my Product Tax Class ID 
        }
    }
}

My product includes the TAX . Right now, when I switch to BE , I m getting this:

My grand and subtotals contains the product price including tax + the Tax, not sure why ?

Do you have any idea about how to approach this ?

Thanks