I’m new to paddle boarding and am looking for my first board. Most of all I want the board to be stable, and I think I mostly will use it in flat water. I want the oportunity to do longer, and maybe also overnight trips so I want one with more space for luggage. I found a good review of Hydra Force Aqua Cruise, and this has space for storage both in the front and in the back. Hydro Force Aqua Cruise 10.6 Inflatable Paddle Board | 2021 Have someone tried this board? Do you recomend other boards with the extra space for storage?
What do you think you could really carry on a SUP?
Not much, but a board with as much storage as possible 
Boards don’t have storage compartments, but instead would be large enough to carry the extra weight and have tie does. The “luggage” you would use would be dry bags strapped to the top of the board in front and behind you.
Do a search on “SUP touring” and you will find articles and videos on how to do it. Might be good to have this background before buying a SUP.
I would focus on getting a decent board that fits your paddling style and the type of water you want to paddle in. Any board can have bungee attachment points added to carry gear. Dry bags are easy to come by. Since paddleboards are a hot commodity right now there are a lot of fly by night companies making boards of questionable design and construction. I have never heard of the brand of board you mentioned. I always caution against buying a boat or board for the “what if” scenario - buy something that works well for how you plan to use it 90% of the time. If it doesn’t work for the other 10% you may find that a second, more specialized board is needed, but I wouldn’t compromise everyday performance for the occasional use. (The classic example of this type of thinking is a tandem kayak - I have had a lot of people come in and want to buy a tandem because their partner/kids/friends “might” want to paddle with them occasionally and they think they can just paddle the tandem as a single the majority of the time. Of course you can, but why buy a boat and then not use it in the way it was intended to be used most of the time?)
Brodie’s comments are spot on. Be very wary about the fly by night brands of Chinese junk SUPs that are getting sold lately. I would spend 6 months or so learning how to paddle, and doing very long day trips before deciding to do touring. Then you will have the skills and judgement on what would be a decent board. You should also try commando camping on dry land with just using the food and equipment you can bring in a small backpack. I have done a lot of kayak camping in Mexico and I would never try the same trips on an SUP. I don’t think there are any rules about what you have to do, once you have the skills to make reasonable judgements. When I travel in my car sometimes I take my surf sup along inside my car and go for 20 mile paddles on it on inland lakes, totally the wrong board for job, but I don’t care. This youtube SUP channel from the UK has had some very good videos on SUP touring , remember they are selling boards too though. Get touring and exploring on your paddleboard with SUPboardermag.com and GeoSUP! - YouTube
I agree with @Peter-CA Paddleboards come with extra length and weight for keeping your luggage there is no storage box. There are many bags available in which you can keep your things and accessories. They are waterproof and light luggage bags.