Yes you can, and Go has done exactly that.
Realize the "log" api is bad? Make "log/slog". Realize the "rand" api is bad? Make "rand/v2". Realize the "image/draw" api is bad? Make "golang.org/x/image/draw". Realize the "ioutil" package is bad? Move all the functions into "io".
Te stdlib already has at least 3 different patterns for duplicating API functionality with minor backwards-incompatible changes, and you can just do that and mark the old things as deprecated, but support it forever. Easy enough.