Handling fee is revenue collected by the store. Now that they have a big pool of revenue, they pay their employees from it (the minimum wage you referred to). Read that in context of the next two paragraphs.
WRT cashiers and stockers that was part of the existing business model. The general profit from groceries covered those expenses.
The general profit from groceries does not cover the expense of a different business model of hiring additional employees whose sole job would be to walk around filling orders. Those additional jobs require additional revenue, which the store gets from handling fee.
Are you implying that stores which are NOT charging a handling fee are losing money?
Regardless of whether they have to hire extra staff to pick items, or to develop a website for online ordering, or to deliver these items in their own vehicles, that's an expense they bulk into the cost of running their business. They would then set prices for the goods they sell based on those expenses + whatever markup they choose.
I will point out that grocery stores have been making a record profit since COVID, and a big part of that is because of online ordering (and price-gouging🤫). We're talking companies who don't charge a handling fee, and some who offer free shipping.
At the end of the day, charging a handling fee in excess of the shipping fee, then asking for a tip, is mildly infuriating.