I have Shopify Markets and its ‘Price rounding’ option enabled and the shipping rates from the cart page and the checkout don’t match

If you enable the ‘ Price rounding’ option from Shopify Markets, all the prices from the store (except gift cards) and the shipping rates will be rounded when a different currency than the configured in the primary market is detected. This option can be found inside Markets, under other markets' preferences:

Depending on the currency, there are different rounding rules applied by Shopify and they cannot be customized. Below you can see some examples:

US Dollar: rounded to US$1.00
Euro: rounded to €0.95
Canadian Dollar: rounded to CA$1.00

You can review the documentation article from Shopify at https://help.shopify.com/en/manual/markets/pricing/rounding.

When the ‘ Price rounding’ option is enabled, Shipping Rates Calculator Plus will display the shipping rates exactly as they are configured in your Shopify Admin (without the rounding rules) because the Shopify API does not provide the information on whether the rounding option is enabled or which rounding rule is applied for each market.

In the below example, the primary market is the UK, and the store’s default currency is the British Pound. In this case, the product prices and shipping rates will be displayed exactly as they are configured in your Shopify Admin both on the cart page and checkout:

However, if the primary market is the UK but, for example, another market with Euro is detected, there will be a different situation. In this case, the Shipping Rates Calculator Plus widget will display the exact shipping rates converted to Euro without price rounding, and, in the checkout, the shipping rates will be rounded to €0.95 (the default rounding option for Euro):

As the Shopify API does not provide the information on whether the rounding option is enabled or not, Shipping Rates Calculator Plus cannot display the shipping rates with price rounding for the different Markets and currencies enabled. Instead, we will display the shipping rates exactly as configured in the Shopify Admin.