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DH and I will often do different things at the same time. We'll sometimes sit on the loungers on Deck 4 reading and will go a couple of hours without talking to each other. Or we'll sit somewhere reading and one or the other of us will say we're going somewhere for a few minutes (get a drink, take pictures, go into the hot tub, whatever) which then then turns into a long period of time because they got distracted or interested in something or got into conversation with someone. Unless we've got something planned at a particular time, we never worry - they'll be back eventually; sometimes we don't even really notice that we're alone. We're a couple, happily married for over 27 years but we don't feel joined at the hip so are both perfectly happy to do stuff together or not, depending on how we feel. Many of the activities allow you to interact with others, or not as you choose, whether you're alone or not.
We've had conversations with people at various activities, in the pool, on deck, at the theatre, and events who are cruising single, doing their own thing even though they're with someone, and single parents whose kids won't leave the clubs so who are effectively cruising single for a large portion of the time. It's not always possible to tell who is cruising solo and who is temporarily solo. It's what we love about cruising. You can do as much or as little as you want, with or without others, whether you came solo or are temporarily solo. You can be as sociable as you want to be or won't want to be.
What kind of things can you do solo - pretty much the same as what you can do not solo. Tastings, trivia, pool time, reading in various locations, movies, afternoon naps, port excursions, cooking demos, talks, ship tours, chatting to others, staring out at the ocean, spa, gym. The list is endless.