Actively applying for Fall 2026 internships. Should I cold message a CEO I'm connected with?

So I'm currently in the middle of fall 2026 internship recruiting. I had an interview last week with one company and just landed a technical interview this week with another. The second one actually came from cold outreach I did myself.

Here's my dilemma: I'm connected on LinkedIn with the CEO of an app I genuinely use and really like. He seems super friendly and approachable. Since reaching out literally just worked for me, I'm thinking of messaging him about fall/winter opportunities. I've wanted too for a while but was afraid it wouldn't go anywhere.

Has anyone done something like this? A few things I'm wondering:

1. Would you go straight to the CEO or try to find someone in HR/recruiting first? It's a smaller team
2. How do you frame it without being weird about it? My connection message already mentioned being an actual user of the product
3. Hypothetically, if I ended up with offers from all three, would I have no choice but to accept the CEO one since I directly reached out? I'd honestly feel terrible turning it down. The other companies are bigger and look great on a resume, but working at this company would be a great experience and since its a smaller team, maybe I could get a return internship/ft offer.

Curious what people think, appreciate any advice :)