I haven't caught up on the entire thread, so some of my reply may repeat what others have said. For starters, bienvenu!
Know that perhaps the most important part of the choice is whether you'll go or not. Pick something that fits your needs, interests you, and is convenient enough to keep life from interfering too easily. Picking based on the style is chancy, as there can be large variations between schools (though that's not always the case). That said, some feedback about the three you posted.
The first two both appear to be Yoseikan Aikido (though both have decided not to use that name, either for marketing reasons or because they've split from that base). I know only a little about that style. What's promising about it is that the style does typically include some Judo, which covers one of the big gaps in most Aikido programs: what to do when the other guy gets really close and/or the "aiki" techniques aren't available. The first school doesn't even list that Judo heritage, so based only on the websites (really thin evidence for basing any judgment), I'd give a slight edge to the second school. Know in advance, though, that many Aikido schools (all styles of Aikido can suffer this, to some degree) have a problem, in that they want to train with a self-defense orientation, but are very focused on the philosophy of Aikido, which keeps them away from solutions that clash, which are often the easiest, most reliable solutions. This also leads many of them to never really train strikes, so you get no tools from that area, and are practicing against bad "attacks".
I know nothing about Ninjutsu, so can speak nothing to that third site, except to say the website didn't really give me any reason to think they teach anything about actually fighting (which is what self-defense is, when we get to the point of actually defending).
In my last dojo, there were free time to actually fight. The art was non-competitive, but during that free time, people would put on a helmet and other protection and get at each other. I agree that simply practicing katas isn't very helpful in real life. So I guess I'll look for a dojo that at least offers this possibility. Or I'll take up Muay Thai haha!
Thank you for your answer!
There's real value to competition. You don't have to compete yourself to see some of that value (though that helps) - being in a school where others compete means you have folks around you who know what works against skilled people from actual practice. Competition also tends to thin out the selection of tools, so you know where to focus. It's even possible to compete without really training with a competition focus, as long as you're not trying to win tournaments. You can just go in to see how your training works for you in that context. I trained most of my life in non-competitive dojos, and am now an advocate for having some competition along the way. At the very least, that should be good sparring in the dojo. For advanced students, that should at least expand to sparring/rolling with folks from other styles, even if informally.
So, for better results, you'd like to have some competitors to train with. When training with a self-defense focus, it's also helpful to train with those who will need the skills on a regular basis "in the street" - cops, bouncers, etc. This will give another kind of feedback, something quite different from competition, that will inform your focus in training.
To be very clear, if you're just looking for something cool that you'll enjoy, any style that suits your fancy will work. If jujutsu appeals to you, by all means, have fun and enjoy yourself. A lot of great reasons to do it. Just don't confuse the sales pitch with the product.
This is important, Charbel. Self-defense is not a thing. As you used the term self-defense orienation in your OP, I suspect you already get this. But just to reinforce, self-defense training is either about fighting, or about avoiding the situations (de-escalation, awareness, choices, etc.). When we talk about physical training for self-defense, we're talking about training to fight off an attack. So, you're training to fight. There's a lot of good marketing out there about "we don't fight", and that's valid if what they mean is they develop the confidence to walk away from potential fights (like in a bar, road rage, etc.). Beyond that, it's just marketing.
The problem you have with not competing is you struggle to mix with people who are any good.
And good at fighting is seriously 90% of self defence. (When it comes to self defense fighting there is a whole staying out of fighting aspect)
The easiest way to break that cycle of being a specific rules based fighter, or BJJ butt flopper is to do different competitions so that you have to manage different circumstances.
Self defense is a puzzle. You get all these solutions to solve only certain parts. And if your solve enough. You get to go home.
This. And the principle is the same even if you don't enter formal competitions. Don't always "spar" with the same ruleset, nor always against folks who trained with you. The more you vary them, the more contexts you're testing out.