We have been on 7 cruises, 2018-2025, 6 on Royal Caribbean ships (4 different ships) and 1 on Norwegian. On most cruise ships, including all 5 that we have been on, guest life jackets are not stored in guest rooms under the beds. They are stored in large cabinets at muster stations. All guests are assigned a specific muster station that you are to go to if the emergency signal sounds. That is thought to be better practice because if there was an emergency guests could be anywhere on the ship so to make them go back to their room to get their life jacket then on to their muster station would take A LOT of time and would be a lot more dangerous than having guests go directly to their muster station.
The cabinets that the life jackets are stored in can only be opened by staff. There may be life jackets stored in other places on the ship. For example, I don't know if the staff's life jackets are the ones in the muster station cabinets or if they're located in a "behind the scenes" location(s).
Anything being thrown overboard, for instance a body, is going to be seen by security immediately. There are hundreds of cameras, and I believe as an added safety measure there are alarms if anything goes overboard. You would need a massive conspiracy involving a large number of staff for a body to go overboard during a cruise and not have an alert immediately occur.
IMO it would be possible for a body to be transported from one location to another without being seen. The challenge here is that it has been reported that her body was discovered at 11:xx am. That is prime time for people moving around the ship. If we were talking 3am it's possible to move around the ship without seeing many people. This ship had around 3900 guests, likely around 1100 crew. I don't see any plausible way a body could be moved around at that time of day. Of course the other thing is that at that time of day the movements of one or a couple people will blend in with everybody else. At 3am security cameras could practically follow a person anywhere on the ship if they wanted to.
One question I have is "was she sharing a cabin with another person or persons", and if so what were the movements of all of those people on that morning. The vast majority of cruise passengers are in double occupancy rooms or suites. This ship likely has around 1900 guest cabins, and I suspect less than 25 of those are designed for single passengers. Some single guests will book a double room. But this being a family trip I'd be surprised if Anna was in a single room.
I suspect this will be solved pretty quickly. LE will focus on the cameras for that corridor of the ship, find out if she entered that room alone or with someone else, and see who went in/out of that room in the 24 hours around when her body was discovered.