Based on my recent experience, and some prior experience that's not all that relevant (pre covid-19), it seems the drivers pretty much do what they please, although not more than advertised by the store.
So if the store says, as some used to, that they will bring it in to your home, then some drivers would, and some wouldn't.
Bringing in, in this context, probably means bring in to your home - the not carrying stuff up stairs inside your home is an old thing, practically all companies that deliver anything have such a clause.
After my last Sainsburys delivery, where the driver left my shopping outside the building my flat is in, I received an email from Sainsburys, a current one that informed me that I was on their priority list, at the behest of the government. This informed me that their drivers would no longer be able to bring shopping into my home, but if I lived in a flat they would bring it to my flats front door. But the previous delivery, a few days before, had refused to even enter the building, stating it was not allowed for him to do so now.
So whether the previous delivery driver had misunderstood the new rules, or simply didn't want to bring it up the stairs I don't know. If the later I don't know if he simply did not want to climb the stairs but was using the virus as an excuse, or if he was genuinely concerned about entering the building.
It doesn't really matter why he refused and left my shopping essentially on the street (I've had the odd one before this that refused to carry them up the stairs and hung around looking bored while I carried stuff up the stairs, when I couldn't even stand up, bend or twist - some people are 'unhelpful' even when it's their job to be helpful.
In my experience there is no point in trying to explain or negotiate with them, the few that won't do their job, as described in the offer of a delivery service to you the customer by the company they work for, don't care what you say, what's wrong with you, or how much of a 'problem' they are causing.
So, hopefully you won't need to, hopefully the driver will bring your shopping to your front door, knock, and the leave, but you should be prepared that you may need to lift it up the stairs - stressful waiting to find out, and not good if you have to - but better than being caught on the hop, like I was.