docs(timeutil): revise timeutil documentation for clarity and examples

Updated documentation for the timeutil module to clarify its compatibility and usage examples.

Author: haithium

docs/src/timeutil/index.md

@@ -3,23 +3,34 @@
 `timeutil` is a C-backed Lua module for wall-clock time, monotonic time, and
 blocking sleep.
 
-It lets Lua read Unix wall-clock timestamps, measure elapsed monotonic time, and
-pause execution for a duration.
+Compatible with Lua 5.1, 5.2, 5.3, 5.4, 5.5, and LuaJIT.
 
-## Compatibility
+Use `timeutil` to read Unix wall-clock timestamps, measure elapsed monotonic
+time without wall-clock jumps, and sleep for fractional-second durations.
 
-`timeutil` supports:
+## Install
 
-- Lua 5.1
-- Lua 5.2
-- Lua 5.3
-- Lua 5.4
-- Lua 5.5
-- LuaJIT
+::: code-group
 
-## Use Cases
+```sh [LuaRocks]
+luarocks install timeutil
+```
 
-- Get Unix wall-clock time from Lua.
-- Measure elapsed time without wall-clock jumps.
-- Sleep for fractional-second durations.
-- Write timing, polling, timeout, and benchmark code.
+:::
+
+## Quick Start
+
+::: code-group
+
+```lua [exmaple.lua]
+local time = require "timeutil"
+
+local start = time.mono()
+time.sleep(0.05)
+local elapsed = time.mono() - start
+
+print(("elapsed: %.3fs"):format(elapsed))
+print(("now: %.3f"):format(time.now()))
+```
+
+:::