docs: replace lingering Gitter links

PR-URL: #9255
Ref: #8923

Reviewed-by: Philipp Burckhardt <[email protected]>

Author: batpigandme

etc/typedoc/index.md

@@ -72,7 +72,7 @@ Thank you for being a part of our community! Your support is invaluable to us!
 -   [**Google Calendar**][stdlib-public-calendar]: calendar of public events, including [open office hours][stdlib-office-hours].
 -   [**Open Collective**][open-collective-stdlib]: financially support the project.
 -   [**Bluesky**][stdlib-bluesky]: follow us on social media.
--   [**Gitter**][stdlib-gitter]: chat with project maintainers and other community members.
+-   [**Zulip**][stdlib-zulip]: chat with project maintainers and other community members.
 
 ## Features
 
@@ -592,7 +592,7 @@ Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].
 
 [stdlib-bluesky]: https://bsky.app/profile/stdlib.io
 
-[stdlib-gitter]: https://gitter.im/stdlib-js/stdlib
+[stdlib-zulip]: https://stdlib.zulipchat.com
 
 [@stdlib/math/base/special]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special
 

etc/typedoc/theme/partials/footer.hbs

@@ -65,7 +65,7 @@
         /
         <a href="/docs/api/">Docs</a>
         /
-        <a href="https://gitter.im/stdlib-js/stdlib">Chat</a>
+        <a href="https://stdlib.zulipchat.com">Chat</a>
         /
         <a href="https://x.com/stdlibjs">X</a>
         /

lib/node_modules/@stdlib/_tools/scripts/publish_packages.js

@@ -519,8 +519,8 @@ function mainRepoSection( customLicense, branch, hasBundles, hasCLI ) {
 		'',
 		'-->',
 		'',
-		'[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg',
-		'[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im',
+		'[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg',
+		'[chat-url]: https://stdlib.zulipchat.com',
 		'',
 		'[stdlib]: https://github.com/stdlib-js/stdlib',
 		'',