Declaration modifiers don't mention the public visibility

The Modifiers section of the Definitions chapter does not mention the public visibility:
https://github.com/leanprover/reference-manual/blob/986f6e92210cd96ede07c8a78317b0b998130eb2/Manual/Defs.lean#L51

Later in that section, it suggests that public is the default visibility:
https://github.com/leanprover/reference-manual/blob/986f6e92210cd96ede07c8a78317b0b998130eb2/Manual/Defs.lean#L83

That second case probably assumes outside a module, but since it already mentions modules, this is confusing. In particular after having read the previous chapter about Modules:
https://github.com/leanprover/reference-manual/blob/986f6e92210cd96ede07c8a78317b0b998130eb2/Manual/SourceFiles.lean#L348

Create a lake library project with lake new foo lib, then add module at the top of Foo/Basic.lean and def test := hello at the bottom of Foo.lean (removing comments), resulting in the following file contents:

% cat Foo.lean
import Foo.Basic
def test := hello
% cat Foo/Basic.lean 
module
def hello := "world"

% lake build
error: Foo.lean:2:12: Unknown identifier `hello`

Adding the public modifier to hello fixes the build:

% sed -i 's/^def/public def/' Foo/Basic.lean
% lake build
Build completed successfully (4 jobs).

Start with the Modifiers section in Manual/Defs.lean around lines 51 and 83, then compare its wording with the module behavior described in Manual/SourceFiles.lean around line 348. Reproduce the provided lake project and build commands to confirm the visibility distinction. Done means the Definitions chapter clearly documents public visibility and its interaction with modules.