Not quite a tote bag, but I have the Sherpa brand carrier for taking my cats out in the car or to the vet. I’ve seen them on sale occasionally and places like petco also have them.
Brought cats in-cabin to Hawaii from the mainland in January 2022. I used these carriers and they were totally fine. They are "airline approved" and soft so they can mold to the area under the seat. Just make sure that your pet plus carrier are under 25 pounds! If you have any questions about all the medical stuff or paperwork, feel free to DM me. It's all still pretty fresh in my memory.
Currently, Hawaiian and Alaska Airlines are the only airlines you can fly a pet in-cabin to Hawaii (just to clarify for the thread in general).
That should work. I've never used it but I know someone who has something like that. They can hide inside if they are scared, but can still see out. I don't really like backpacks because they pretty much have to be in a standing position.