Slightly smaller 8 year age gap here. Yes, the older one gets annoyed sometimes by the little one. And the little one gets frustrated and deliberately irritates his big sis. But they adore each other. They are definitely siblings and share silly jokes and games.
Activities that work okay for us are beach holidays, forest walks, trips to some "big" museums like vehicle museums, aircraft displays, Christmas markets, fairgrounds
and circuses, trips to the local library, baking and cooking (surprisingly successful), cycling (from 6 months baby can go in a seat on back of an adult's bike), swimming, gardening, visiting grandparents, eating out. Loads of stuff.
I tried very hard not to give big sister responsibility for the little one when they were tiny as I didnt want her to feel exploited.
It works pretty well in reality. The bigger one needs you less, and can wait more patiently if you are busy with the baby. Squabbles blow over very quickly. They don't argue too much over toys and there isn't really any jealousy as they want you in different ways and usually at different times.
My DD gained a lot of independence and maturity from having a little brother and has decided she wants to be a teacher when she grows up, she loves showing her little brother things and seeing him grow and learn.
I wouldn't have it any other way.