There is a TON of research on ML algorithms for all this!
For facial rec-
BearID project - http://bearresearch.org/ (individual facial rec for grizzlies)
AnimalFACS (facial action coding system) - http://www.chimpfacs.com/ (the model started with chimps but they now have versions for orangutans, gibbons, macaques, dogs, cats, and horses)
A lot of the gesture/facial expression literature is focused on primates, particularly apes, so if you do a Google Scholar search on that, you'll loads of papers that have looked into this as well.
For vocals -
Carlson, N. V., Kelly, E. M., & Couzin, I. (2020). Individual vocal recognition across taxa: a review of the literature and a look into the future. Philosophical Transactions of the Royal Society B, 375(1802), 20190479.
Turesson, H. K., Ribeiro, S., Pereira, D. R., Papa, J. P., & de Albuquerque, V. H. C. (2016). Machine learning algorithms for automatic classification of marmoset vocalizations. PloS one, 11(9), e0163041.
Wijers, M., Trethowan, P., Du Preez, B., Chamaillé-Jammes, S., Loveridge, A. J., Macdonald, D. W., & Markham, A. (2020). Vocal discrimination of African lions and its potential for collar-free tracking. Bioacoustics, 1-19.
Clink, D. J., Crofoot, M. C., & Marshall, A. J. (2019). Application of a semi-automated vocal fingerprinting approach to monitor Bornean gibbon females in an experimentally fragmented landscape in Sabah, Malaysia. Bioacoustics, 28(3), 193-209.
Spillmann, B., van Schaik, C. P., Setia, T. M., & Sadjadi, S. O. (2017). Who shall I say is calling? Validation of a caller recognition procedure in Bornean flanged male orangutan (Pongo pygmaeus wurmbii) long calls. Bioacoustics, 26(2), 109-120.
Hantke, S., Cummins, N., & Schuller, B. (2018, April). What is my dog trying to tell me? The automatic recognition of the context and perceived emotion of dog barks. In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 5134-5138). IEEE.
Totakura, V., Janmanchi, M. K., Rajesh, D., & Hussan, M. T. (2020). Prediction of Animal Vocal Emotions Using Convolutional Neural Network. International Journal of Scientific & Technology Research, 9(2), 6007-6011.
Neethirajan, S., Reimert, I., & Kemp, B. (2021). Measuring Farm Animal Emotions—Sensor-Based Approaches. Sensors, 21(2), 553.
Hong, W., Kennedy, A., Burgos-Artizzu, X. P., Zelikowsky, M., Navonne, S. G., Perona, P., & Anderson, D. J. (2015). Automated measurement of mouse social behaviors using depth sensing, video tracking, and machine learning. Proceedings of the National Academy of Sciences, 112(38), E5351-E5360.