works in insert mode, but redo doesn't work (neither in normal nor insert mode)

redo could be implemented as such: put the contents in the drop register, and add "~p (resp. <c-r><c-o>~ ) to the redo buffer. But it won't work if one puts several different texts during the same insert mode.

Alternatively consider it a low-level primitive and let redo be implemented by the plugin using this. But "~ would make sense for UI initiated put.

But it won't work if one puts several different texts during the same insert mode.

Could it be a linked list?

BTW where is insert-mode implied? What happens if nvim_put is called in some other mode?

implied how? It just doesn't do anything special on insert mode (except CURSEND on the latest push). Make "~ a linked list how? Or yet a set of numbered registers?

What happens if nvim_put is called in some other mode?

It does what we want it to do. In visual mode we can either do nothing special (except adjusting cursor/VIsual afterward), most flexible for plugins, or simulate the delete implicit in vp, most convenient for UIs. I guess in cmdline mode it should also emulate <c-r><c-r>.