How many days could be considered enough for full adoption of a new work environment and corporate culture?

Management Science is considering 18 months and more, taking for example "John Kotter's 8-Step Process for Leading Change" into account. It now depends, if your question is only focusing on the (full) personal adoption, or if the new culture has settled across all business units and further departments, which may even take a few years until old culture and behavior vanishes. It is also highly effected by supporting actions during the change or if employees are just left alone with the new situation (which unfortunately is quite common currently).

On an average I have observed it take 2 to 3 months.

I don't know this can be quantified because the variable is what you are adopting and the size of the organization. Small org, small changes, quick. Large org, big changes, slow. There's plenty of research on change, but not single source of truth.