I was wondering if there is any statistical equivalence test (in r or python) for multinomial data "a contingency table (4x4)" to know whether the observed and the expected values are equivalence?
Yes, there is one. Please, look at my papers https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2907258 and https://www.researchgate.net/publication/312481284_Testing_equivalence_of_multinomial_distributions. The implementation is also available on github. Do not hesitate to ask me if any questions occur.