You can't shadow a CEO but you can read books written by those who have. Try reading the biographies of Jobs or Musk by Walter Isaacson. He had long term access to them and shadows them throughout their day for years.
You can argue that these two aren't representative and put in more effort than the average CEO, but you can't argue that their experience of being CEO isn't extremely intense.
Good CEOs are constantly juggling all kinds of complex thought-work, to a much greater extent than the average line worker would be happy doing. Programmers in particular get stressed and unhappy if you ask them to context switch between unrelated tasks, deal with interruptions and regularly make decisions that are completely ambiguous. They also probably won't be happy if they have to spend a lot of time on relationship building, performance evaluations or managing the performance of people under them.
A good CEO's typical day will easily switch between a dozen different things - a product review in the morning where they're expected to give immediate and ideally insightful feedback to a team that's been preparing for months (remembering to manage their own expectations and happyness, you wouldn't want your star designer quitting on you), then immediately after a meeting with the finance team about some complicated tax issue, and then a recruiting call with someone to replace the head of sales who you just had to fire because they {missed their targets, leaked confidential info to the press, insulted a key customer, got targeted by a woke mob} and then you move on to lunch, briefly, which you probably eat alone because none of your immediate reports particularly want to hang out with the boss and anyway you need to read a report on your competitor's new product launch. Oh and then it's time to go to the airport because {a key customer the other side of the country is upset, the government is demanding to question you, your PR team set up a speaking event at a conference and only told you yesterday}, so hopefully your spouse isn't too upset that you won't be home for dinner tonight. On the way to the airport you'll have to be on the phone with a lawyer because your company is getting sued, again, and so you need to know the status of the case but couldn't find time to fit an in-person meeting (which you'd have much preferred). You'll probably also need to plan for how to pay if you lose that case, which realistically means who you'll have to lay off or break comp promises to.
And then dawn breaks, and it all begins again. That's a good day, when you didn't have to do layoffs or explain to the board why the new product you'd hoped would turn things around is now subject to a recall.
I've seen how this stuff affects people up close. You do need to be very tough, and even then it can grind people down pretty catastrophically. There's nobody to blame at that level and you can't just quit because you don't like it anymore. If it starts going wrong you're sort of trapped.