ENH: exclude html table border w/False value
Per the HTML5 spec, border attributes on table elements are obsolete.
Borders should be implemented via CSS instead.
https://html.spec.whatwg.org/multipage/obsolete.html#attr-table-border
This enhancement will retain the default behavior of the border keyword of to_html,
but will exclude the attribute entirely upon receiving a falsy value.

closes  #22692

@github-actions pre-commit Excluding the border attribute upon `border=0` failed this test case: `pandas\tests\io\formats\test_to_html.test_to_html_border`

So I have revised the enhancement to only exclude the border attribute when border=False

**fixed typo
 This is one of the reasons I am trying to push `styler.to_html` as the architecture for `Dataframe.to_html`.

`Dataframe.to_html()` produces other officially deprecated HTML: #39951

Whilst this commit solves this problem, it shouldn't be the long term solution, and its only a half measure since it still allows the old behaviour. can you move the whatsnew note to the I/O section @jreback done This test has failed twice for reasons that I'm unclear on

**Code Checks / ASV Benchmarks**

``` bash
[ 50.00%] ··· ...a.TimedeltaProperties.time_timedelta_seconds           3.80±0μs
Error: Process completed with exit code 1.
``` This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. pls merge master @jreback done thanks @z3c0 