Updated documentation to match doc guide.

[RogerJanusiak]

Here is a full list of changes made when feeding the current docs and DocGuide to claude:

Here is a summary of every change made across the four files, organized by guideline:

index.md

Rewrote intro paragraph — removed informal "But it also", tightened phrasing
Fixed typo "Instalation" → "Installation"
Replaced "See detailed usage here:" with impersonal "Detailed usage is available in"
Removed informal "easily" from to_awk() description; rewrote as present-tense declarative
installation.md

Fixed typo "endpoit" → "endpoint"
Replaced "you can verify" with impersonal "the package can be verified by running"
file_introspecting.md

Merged redundant intro sentences into one focused paragraph
Fixed double space in ## Overview heading
"python function backend" → "Python function backend"
Changed future-tense phrasing in Parameters ("will be used", "will return", "will print") to present tense
"This will output" → "This outputs"
Added context sentence before the practical output example

JSON input (level 4) → ### JSON Input (level 3), resolving the prohibited heading depth

Fixed typo "datasets.jsosn" → "datasets.json"
Added json language tag to the JSON code block
"Similarly to" → "Similar to"
Fixed typo "structre" → "structure"

Return awkward array type (level 4) → ### Return Awkward Array Type (level 3)

"return their" → "returns their"
"will be applied" → "is applied" (present tense)
"will show as" → "show as" (present tense)
materialization.md

Removed redundant duplicate intro sentence; replaced with single clear purpose statement
"Enables parallel execution" (sentence fragment) → proper sentence
"Return iterators instead…" → "Iterators are returned instead…" (active/impersonal)
"You can then manually loop" → "The data chunks can then be processed" (removed second-person)
"All events can also be loaded by using:" → "All events can also be concatenated into a single array:"
"being passing" → "being passed" (grammar fix)
"homegeneously" → "homogeneously" (typo)
"must point be either" → "must be either" (grammar fix)
"## Multiple samples" → "## Multiple Samples" (consistent heading capitalization)
"will have None" → "has None" (present tense)
"non servicex" → "non-ServiceX"; "inputed" → "provided" (language conventions)

[RogerJanusiak]

This PR is for Issue #43

[RogerJanusiak]

The most recent commit adds the Search bar to the documentation. Unfortunately there is not an easy way to test that the search bar works, but I have used it already in the FuncADL repo and the 15minhist repo. So I know it works!

[ArturU043]

I have a few ideas and comments on changing the content of the docs
But this PR is more about the technical implementation.

Lets merge this and I'll change the contents later on