Bit difficult to make reasonable comments based on the info provided.
For sure it good if batteries last ‘as long as possible’ but that’s meaningless really, what is the practical limit required ? Is a 10minute battery life enough, an hour or a month maybe ?
Same with ‘as small as possible’. You seem to suggest a size similar to a ring door bell, but what size of ring doorbell did you have in mind ?
I believe the smallest of the ESP32 Camera boards in the SEEED XIAO ESP32S3 sense;
Yes, I can do this project. I have done something very similar using XIAO camera. I can also design the enclosure and take care of the APIs. Let's connect at chanchalkks@gmail.com