One week post spay is too soon for them to be together. There are two major reason: One is it takes 2 weeks for spay wounds to heal properly, the other is that a bun gets hormonally unstable for a period after desexing. The body and brain needs to adjust to the stopped production of sex hormones. This adjustment period can last from a couple of weeks to, in some cases, several months. While it’s going on, the rabbit can exhibit extra hormonal behavior, for example territorial poop and pee-marking, territorial aggression, corting or jumping etc. It’s perfectly normal and it’s temporary.
Your newly spayed bun can have play time outside the cage now, but you’re right in that she shouldn’t run (or jump) and she shouldn’t be with her sister due to the risk of (hormonally induced) fighting. You can let them be in the same room of course and also swap toys between them, but wait at least a week more before you try to reintroduce them. Their chances of forming a solid and harmonious adult bond are much higher if you take things slowly.
Many continued safe healing vibes for your youngest!