Cortana is loved by the comunity for her big “brains” if you know what i mean . It makes sence that she could project herself as a solid. and even in the books they say that ai’s can change what they look like on a wim. halo 1 short hair halo2 it gets longer, and soshe looks fine and as i said befor she could be displaying herself in hard light. she could already project herself in halo 3. she did this to show the chief how to start the 4th halo . but if she got all the knowlege from the 4th halo ring, then she would then know how to project herself with a sustaind power source. not only that the forerunners made their ships in this manner. they traped chakka in hard light to take him to the 7th halo. primodeom greag bear. read the books they are telling you to do so “343 frankie” all this makes sence once your in the know. not to mention their are still hurgks alive from the forerunner times aka enginers. they pimped lucys’ suit with wait for it forerunner vision and better hearing etc.
All this has to be taken into account. it/she is a smart ai and can do amazing things. Now she understainds a lot of information. and is verce in forunner tech . hard light is a parler trick to them and is how they construct everything . i’ll leave you with this to ponder how and why the change. But with some research it will make sence.