build(deps): bump rich from 13.9.4 to 14.1.0 in /tools/publish (#3230)

Bumps [rich](https://github.com/Textualize/rich) from 13.9.4 to 14.1.0.
<details>
<summary>Release notes</summary>
<p><em>Sourced from <a
href="https://github.com/Textualize/rich/releases">rich's
releases</a>.</em></p>
<blockquote>
<h2>The Lively Release</h2>
<p>Live objects may now be nested. Previously a progress bar inside
another progress context would fail. See the changelog below for this
and other changes.</p>
<h2>[14.1.0] - 2025-06-25</h2>
<h3>Changed</h3>
<ul>
<li>Removed <code>typing_extensions</code> from runtime dependencies <a
href="https://redirect.github.com/Textualize/rich/pull/3763">Textualize/rich#3763</a></li>
<li>Live objects (including Progress) may now be nested <a
href="https://redirect.github.com/Textualize/rich/pull/3768">Textualize/rich#3768</a></li>
<li>Added padding property to Syntax which returns a tuple of four
integers <a
href="https://redirect.github.com/Textualize/rich/pull/3782">Textualize/rich#3782</a></li>
</ul>
<h3>Fixed</h3>
<ul>
<li>Fixed extraction of recursive exceptions <a
href="https://redirect.github.com/Textualize/rich/pull/3772">Textualize/rich#3772</a></li>
<li>Fixed padding applied to Syntax <a
href="https://redirect.github.com/Textualize/rich/pull/3782">Textualize/rich#3782</a></li>
<li>Fixed <code>Panel</code> title missing the panel background style <a
href="https://redirect.github.com/Textualize/rich/issues/3569">Textualize/rich#3569</a></li>
</ul>
<h3>Added</h3>
<ul>
<li>Added <code>TTY_INTERACTIVE</code> environment variable to force
interactive mode off or on <a
href="https://redirect.github.com/Textualize/rich/pull/3777">Textualize/rich#3777</a></li>
</ul>
<h2>The ENVy of all other releases</h2>
<p>Mostly updates to Traceback rendering, to add support for features
introduced in Python3.11</p>
<p>We also have a new env var that I am proposing to become a standard.
<code>TTY_COMPATIBLE=1</code> tells Rich to write ansi-escape sequences
even if it detects it is not writing to a terminal. This is intended for
use with GitHub Actions / CI, which can interpret escape sequences, but
aren't a terminal.</p>
<p>There is also a change to how NO_COLOR and FORCE_COLOR are
interpreted, which is the reason for the major version bump.</p>
<h2>[14.0.0] - 2025-03-30</h2>
<h3>Added</h3>
<ul>
<li>Added env var <code>TTY_COMPATIBLE</code> to override auto-detection
of TTY support (See console.rst for details). <a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
</ul>
<h3>Changed</h3>
<ul>
<li>An empty <code>NO_COLOR</code> env var is now considered disabled.
<a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
<li>An empty <code>FORCE_COLOR</code> env var is now considered
disabled. <a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
<li>Rich tracebacks will now render notes on Python 3.11 onwards (added
with <code>Exception.add_note</code>) <a
href="https://redirect.github.com/Textualize/rich/pull/3676">Textualize/rich#3676</a></li>
<li>Indentation in exceptions won't be underlined <a
href="https://redirect.github.com/Textualize/rich/pull/3678">Textualize/rich#3678</a></li>
<li>Rich tracebacks will now render Exception Groups <a
href="https://redirect.github.com/Textualize/rich/pull/3677">Textualize/rich#3677</a></li>
</ul>
</blockquote>
</details>
<details>
<summary>Changelog</summary>
<p><em>Sourced from <a
href="https://github.com/Textualize/rich/blob/master/CHANGELOG.md">rich's
changelog</a>.</em></p>
<blockquote>
<h2>[14.1.0] - 2025-06-25</h2>
<h3>Changed</h3>
<ul>
<li>Removed <code>typing_extensions</code> from runtime dependencies <a
href="https://redirect.github.com/Textualize/rich/pull/3763">Textualize/rich#3763</a></li>
<li>Live objects (including Progress) may now be nested <a
href="https://redirect.github.com/Textualize/rich/pull/3768">Textualize/rich#3768</a></li>
<li>Added padding property to Syntax which returns a tuple of four
integers <a
href="https://redirect.github.com/Textualize/rich/pull/3782">Textualize/rich#3782</a></li>
</ul>
<h3>Fixed</h3>
<ul>
<li>Fixed extraction of recursive exceptions <a
href="https://redirect.github.com/Textualize/rich/pull/3772">Textualize/rich#3772</a></li>
<li>Fixed padding applied to Syntax <a
href="https://redirect.github.com/Textualize/rich/pull/3782">Textualize/rich#3782</a></li>
<li>Fixed <code>Panel</code> title missing the panel background style <a
href="https://redirect.github.com/Textualize/rich/issues/3569">Textualize/rich#3569</a></li>
</ul>
<h3>Added</h3>
<ul>
<li>Added <code>TTY_INTERACTIVE</code> environment variable to force
interactive mode off or on <a
href="https://redirect.github.com/Textualize/rich/pull/3777">Textualize/rich#3777</a></li>
</ul>
<h2>[14.0.0] - 2025-03-30</h2>
<h3>Added</h3>
<ul>
<li>Added env var <code>TTY_COMPATIBLE</code> to override auto-detection
of TTY support (See console.rst for details). <a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
</ul>
<h3>Changed</h3>
<ul>
<li>An empty <code>NO_COLOR</code> env var is now considered disabled.
<a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
<li>An empty <code>FORCE_COLOR</code> env var is now considered
disabled. <a
href="https://redirect.github.com/Textualize/rich/pull/3675">Textualize/rich#3675</a></li>
<li>Rich tracebacks will now render notes on Python 3.11 onwards (added
with <code>Exception.add_note</code>) <a
href="https://redirect.github.com/Textualize/rich/pull/3676">Textualize/rich#3676</a></li>
<li>Indentation in exceptions won't be underlined <a
href="https://redirect.github.com/Textualize/rich/pull/3678">Textualize/rich#3678</a></li>
<li>Rich tracebacks will now render Exception Groups <a
href="https://redirect.github.com/Textualize/rich/pull/3677">Textualize/rich#3677</a></li>
</ul>
</blockquote>
</details>
<details>
<summary>Commits</summary>
<ul>
<li><a
href="https://github.com/Textualize/rich/commit/2dca1b70359dac61e1bbfb6f14ebe19a5ab79c3d"><code>2dca1b7</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3808">#3808</a>
from Textualize/bump1410</li>
<li><a
href="https://github.com/Textualize/rich/commit/19b6dddd807b887eaaf313174fff3eb2e22cda25"><code>19b6ddd</code></a>
version bump</li>
<li><a
href="https://github.com/Textualize/rich/commit/a75a9a9838814cffb68cefe3522fc47c8ddce768"><code>a75a9a9</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3807">#3807</a>
from Textualize/optimize-options</li>
<li><a
href="https://github.com/Textualize/rich/commit/9a08a2d3a983591e2d0d46e4f63558dd8df9e47d"><code>9a08a2d</code></a>
optimize size</li>
<li><a
href="https://github.com/Textualize/rich/commit/9c9b011187bba772dca57653c9114005b489f005"><code>9c9b011</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3680">#3680</a>
from Textualize/willmcgugan-patch-1</li>
<li><a
href="https://github.com/Textualize/rich/commit/56855a6b81befafa6e978cffed4c1fb389a20df0"><code>56855a6</code></a>
Update bug_report.md</li>
<li><a
href="https://github.com/Textualize/rich/commit/fa9ce3ce70c22ea2bb83dbd1f867fe90d1b3f0c5"><code>fa9ce3c</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3692">#3692</a>
from smacke/null-tb-offset-fix</li>
<li><a
href="https://github.com/Textualize/rich/commit/e0c7e96b303e6f3e48818380527129fb21f453f3"><code>e0c7e96</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3783">#3783</a>
from Textualize/live-typing</li>
<li><a
href="https://github.com/Textualize/rich/commit/81b12554b3b15374aa48dae3f6507202bd8fab3e"><code>81b1255</code></a>
Self typing</li>
<li><a
href="https://github.com/Textualize/rich/commit/21b3800894f6a81d3f68a0e34796be67e3ccd39f"><code>21b3800</code></a>
Merge pull request <a
href="https://redirect.github.com/Textualize/rich/issues/3718">#3718</a>
from TomJGooding/fix-panel-fix-title-missing-panel-b...</li>
<li>Additional commits viewable in <a
href="https://github.com/Textualize/rich/compare/v13.9.4...v14.1.0">compare
view</a></li>
</ul>
</details>
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