Hello. I am sorry to read about this. It is always so hard to lose a family member.
I have been through a pet or pets having to grieve & will share my experience. The first loss occurred many years ago while the cat was at the emergency clinic & therefore, we did not have him at home & did not bring him home because we decided to have him cremated. Our other cat searched and searched for him which was heartbreaking. I called the vet/breeder we got her from for advice & she asked where the cat who passed was..... She said that if we had brought him home it would have made it easier for her. I kept that advice in mind and years later when she passed, I brought her home. We have Nest cams and it was fascinating to watch how the other cats managed the loss. It was pretty similar to what you see at a funeral home viewing. The cats who had less of a relationship went over, sniffed her and moved on pretty quickly. The ones, and particularly the one, who had a super close relationship with her, waited until everyone else was out of the room, including us, and then went in. He sat with her for a very long time before deciding to leave. It was SO hard to watch, but did make a difference for him. I would say he did still grieve, but he was not searching for her, smelling the floors etc like she had done years ago trying to figure out where her family member went. He knew what happened.
I have a friend who also brought her cat home and the sister of the cat who passed did the opposite. They were super close, but the sister did not want to come near the cat who passed and just looked and took off to another room. She still at least knew what had occurred but managed it differently than my cat. Very similar to what we often see at visitations. Some people do a quick pass, while others wait for a moment when they can spend a little more time with the deceased alone.
I would assume, that like people, each cat manages the process differently. However, I do believe that the vets advice that bringing or having the cat who passed at home so that the other cat(s) know that the sibling or bonded cat has passed, does make a significant difference in their ability to move on because they at least know what happened. It is a less complicated grieving process. They can skip over the stress of “where did they go” and search process.
We did make sure to do some extra play time, be at home and give extra attention to the rest of the group, especially the cat who was close with her, & that seemed to help as well.
Thoughts and prayers to you. -Amy