For instance, can I personally own the domain names, the trademarks, and the code of all the SaaS companies I have created without carrying any liability for their operations? Does this have to be stated somewhere explicity, or is implicit (i.e., if I haven't assigned it to any legal entity, I own it under my own name)?
In such a scenario, if any of my SaaS companies got sued for something, what assets would they still risk losing? Only the data?
But generally, yes, you personally can own the rights to things your company uses, and you can take "royalty" or "license" payments from the business for those, which is a different type of income versus salary. Much like you can rent office space to your company and that is also treated differently tax wise. To be clear though, most of the time you don't want to own the technology behind the business because if it is deemed faulty and causes a major problem or has a major security bug etc a client can sue not just the business but you personally for all your assets since it is your direct property and that will move forward in court, you will get no personal protection. The corporation is there to protect your personal assets, you get none of that protection if you own the assets the corporation uses, in fact you make yourself a target instead.
At the extreme end, if the company is but a shell and you own everything personally the courts could rule your corporation is invalid and not the true legal entity and so they could strip the company and you of the protections. There are a ton of rules around this that a competent, experienced business attorney needs to advise you on.
Frankly if you are not even in business yet and aren't making money you are worrying about the wrong problem, get customers, get business, make something, then optimize corporate structure once things are really moving and you have income coming through the door. Because until the company is making more then it is losing no one is generally going to sue and spend money on attorneys to get nothing in return. They might sue to get the assets but even then that is really rare, and usually most larger businesses will force you to vault your product anyway in case you go under as their protection so they don't need to sue.