I used to work on a regional grocery chain's website (in the Southern USA) for online ordering and fulfillment. It's a constant battle. Consider the sheer number of products on store shelves. The average number of products is 30k+. Now, consider that some percentage of those are constantly in flux and potentially unique per store. Holiday items, promotions, marketing from suppliers, overflow, etc etc. Anytime a price is changed or a product brought in/out of stock, that line in the database needs to be updated. Product images and nutrition information can also be in flux as companies adjust their products in response to supply chain or financing particulars.
At the end of the day, gathering and aggregating all of that crap into a stable API is a chore unto itself. Multiple people's jobs. Updating products, associating taxonomies, in-store locations, duplicate locations, optimizing pickup routes, etc etc etc. There is a lot of grunt work here that can't be entirely automated away when dealing such a dynamic business.
Now you need to build a website that takes all of this data and somehow displays it in a format that is comprehensible and accurate for consumers. Showing relevant recommended products, search keywords, cache and image management (for potentially resizing dynamic supplier photos). Then think about the cart and checkout, two areas and Shopify and Amazon have devoted literal billions of dollars to optimize. Your volume is big enough that using an off the shelf payment provider is off the table; not to mention that you don't have the margins anyway. Have you thought about mobile apps and the development effort required there as well?
Grocery stores are hard enough as is but doing them online is a totally different beast. There's a reason that all of the "Kroger" brands use the same exact website with a different logo in the corner. The only players in this space doing it reasonably well are huge conglomerates with money to burn on building the required infrastructure to build the audience. Actually, I just looked up Harris Teeter and they appear to be a Kroger brand as well. TIL. I would say that "Kroger" is one of the better ones. Whole Foods is also doing decently well if you can afford the price premium, but I realize for most people that isn't a luxury they can afford.
The best way to get them to improve is to keep using the service and demanding better (or use a competitor if available). These departments have KPIs. If you get the wrong product, file a complaint at the end of your order process and mark any NPS surveys appropriately. If fulfillment has a lot of bad data from elsewhere in the organization driving their performance scores down, then they are incentivized to get it fixed. I know it sucks, but the only other alternative is to not use it at all and risk is going away forever.