It's not possible. See, the name of tag (any reference, in fact; the same goes with branches) is treated as the name of the file system object, created in $GIT_DIR/refs folder of your repository. This object stores the hash commit the tag is attached to.
With tag foo, it's easy - file foo is created in $GIT_DIR/refs, nothing special to wonder about.
With tag foo/bar, however, it's a bit more complicated: now folder foo is created, having just a single file - bar (again, with the hash commit). Quoting the docs:
[reference names] can include slash / for hierarchical (directory) grouping
The problem is, it's not possible to have two objects - file and folder - with the same name. So if you already have 1.16.0 tag, you won't be able to work with 1.16.0/anything. One obvious solution is transforming that initial tag into something like 1.16.0/0.0.1, then proceeding with your original intent. Or you can just replace slash with - or _.