docs: Fix Verso code blocks and {name} roles

- Add imports to Concepts.lean for code elaboration
- Mark code blocks as ```lean for hover info
- Use full paths for {name} roles (LeanPlot.Components.sample)
- Fix scatter example (remove undefined noise variable)
- Use {name} roles for function references

Author: alok

doc/Manual/API.lean

@@ -20,7 +20,7 @@ tag := "api-reference"
 LeanPlot provides a layered API following {deftech}_progressive disclosure_:
 
 1. *Tier 0 (Zero-Config)*: Functions like {name}`plot`, {name}`plotMany`, {name}`scatter`, and {name}`bar` that just work
-2. *Tier 1 (Components)*: Mid-level functions like {name}`sample` and `mkLineChart` for more control
+2. *Tier 1 (Components)*: Mid-level functions like {name}`LeanPlot.Components.sample` and `mkLineChart` for more control
 3. *Tier 2 (Recharts)*: Direct access to Recharts JSX components for full customization
 
 # Zero-Config Functions
@@ -70,7 +70,7 @@ Create scatter plots for visualizing discrete data points.
 ![scatter example](img/scatter_demo.svg)
 
 ```lean
-#html scatter (fun x => x^2 + noise) (steps := 50)
+#html scatter (fun x => x^2 + 0.1 * Float.sin (10 * x)) (steps := 50)
 ```
 
 {docstring LeanPlot.API.scatter}

doc/Manual/Concepts.lean

@@ -4,9 +4,12 @@ Released under Apache 2.0 license.
 -/
 import VersoManual
 import Manual.Meta
+import LeanPlot.API
+import LeanPlot.DSL
 
 open Verso.Genre Manual
 open Verso.Genre.Manual.InlineLean
+open LeanPlot.API
 
 set_option pp.rawOnError true
 
@@ -28,8 +31,8 @@ while advanced customization is still possible when needed.
 
 The three tiers are:
 
-1. *Tier 0 (Zero-Config)*: One-liner helpers like `plot`, `scatter`, `bar`
-2. *Tier 1 (Components)*: Building blocks like `sample`, `mkLineChart`
+1. *Tier 0 (Zero-Config)*: One-liner helpers like {name}`plot`, {name}`scatter`, {name}`bar`
+2. *Tier 1 (Components)*: Building blocks like {name}`LeanPlot.Components.sample`, `mkLineChart`
 3. *Tier 2 (Recharts)*: Direct JSX access for full control
 
 Most users only need Tier 0. The other tiers exist for when you need
@@ -66,18 +69,20 @@ tag := "plot-command"
 The `#plot` command is defined in `LeanPlot.DSL` and provides convenient syntax
 for plotting functions:
 
-```
+```lean
 -- Basic usage
 #plot (fun x => x^2)
+```
 
+```lean
 -- With custom sample count
 #plot (fun x => Float.sin x) using 400
 ```
 
 Behind the scenes, `#plot f` expands to `#html LeanPlot.API.plot f`.
 
-For expressions that already return `Html` (like `plotMany`), use `#html` directly:
+For expressions that already return `Html` (like {name}`plotMany`), use `#html` directly:
 
-```
+```lean
 #html plotMany #[("sin", Float.sin), ("cos", Float.cos)]
 ```