9 month old puppy biting, unknown training history. What method to follow?

I adopted a 9 month old puppy on Saturday. She was with a foster family for a couple of weeks before I adopted her, so her training was probably nonexistent prior to intake. We believe she was an outside dog as she has trouble regulating herself inside.

She is bitey. I’ve noticed when she’s overtired she becomes extra bitey, and I’ve started enforcing naps or bedtime when this happens.

But, when we’re awake and playing, how should I handle her biting? I’ve found resources for younger puppies, which doesn’t apply because I can’t really walk away from her or leave her in a play pen – she’s too big. I’ve found resources for adults, which might apply but her biggest biting phase happens at 8 pm every night – which to me suggests tantrum and overtired.

If we’re awake and playing, I redirect with a toy and praise when she takes the toy.

What should I do when she goes after my hands and won’t redirect to a toy? Leave the room? She’s too big for a play pen, so I can’t really walk away as she’ll follow. I’ve been hiding my hands. Do I have guests ignore her until she’s calm?

I have family over often, and everyone is treating her differently. I want to know what she needs in order to make sure everyone is on the same page.