Can you reproduce this issue on default Wordpress theme (eg Storefront)?

Yes

Can you reproduce this issue when all other plugins are disabled except WooCommerce, Polylang, and Hyyan WooCommerce Polylang Integration?

Yes

What product versions and settings are you using when this issue occurs?

• PHP: 7.3.6
• WordPress: 5.2.1
• WooCommerce: 3.6.4
• Polylang: Free
• Hyyan WooCommerce Polylang Integration: 1.4.0
• Browser: any

Steps to Reproduce

1. Set up Polylang with at least 2 languages.
2. Create a product in both languages.
3. Install any Woocommerce currency switcher (I used Currency Switcher by Realmag and switcher by algoritmika)
4. Set 2 currencies.
5. Go to the shop and switch to the additional currency (not the default one).
6. Add the product to the cart.
7. Go to the Cart page.
8. Switch to the second language.

What I Expected

The product prices are correct.

What Happened Instead

The prices of products in the cart are not correct.
Although, the subtotal in the Shipping calculator is correct.

This is a bug introduced in pre-release 1.4.0. I tested it now for a few hours.

Also, possible to test here (EURO is the additional currency):
https://www.test2.liberlapidum.com/test2/