Shopify has a coupon that says "Buy X, get Y", but since the customer needs to add the applicable product to their cart, it would be nice to add it automatically if possible. There are many excellent apps available, so I would basically recommend using those, but you can also use Flow to add coupons after purchase.
Using Shopify Flow to implement "Give a free gift when you spend more than XXX yen"

[Setup Step 1] Register the target novelty product (draft is OK) and create a flow to add the product to the order when the amount exceeds a certain amount.

[Settings Step 2] Settings > Notifications > Edit Order > Edit Code (Add a message to be displayed for orders that include the target novelty item)

[Implementation Results] When the total amount excluding shipping exceeds a certain amount, the product is automatically added and an email is sent to inform the customer that the order has been updated.

