To be fair to Grace, I don’t see any evidence of a drink problem. For all the PR events she goes to, with all the free food and drink, it appears she drives to them mainly. If she had a drink problem I’d imagine she’d want to make the most of it and leave the car at home.
She gets up at the crack of dawn (for no reason whatsoever!) and shows no sign of being hungover/groggy. If she was drinking the night before I doubt she’d be up that early for her morning walks.
I think the reason for her slothiness is a combination of laziness and lack of direction in her life, and possibly some mild depression. Getting a regular job would probably be the best thing she could do for herself as it would give her something to focus on, instead of daily reminders of how far her influencing career has fallen.