WordPress has integrated jQuery UI?
The official docs lists that a large amount of jQuery UI is present in core already, and needs only to be enqueued:
https://developer.wordpress.org/reference/functions/wp_enqueue_script/
In the official page of https://codex.wordpress.org do I have an option similar to https://jqueryui.com/ that has add-ons to copy and paste?
No it doesn’t, but that’s because it isn’t necessary. jQuery UI works the same way in WP Admin as it does anywhere else, the javascript works identically. Simply enqueue the script, then use it in your own JS files once the document is loaded as you would anywhere else.
If you require copy pasta, you can get it from jqueryui.com and all the usual places.
I can add libraries like jQuery UI to my plugins without causing any problems in WordPress
As long as you use the library bundled with WordPress core you should be fine. If you try to bundle jQuery UI inside your plugin however, then there can be conflicts, as different versions are loaded at the same time.
The same is true of any code that bundles jQuery, e.g. when developers over-optimise and try to use the CDN jQuery, loading it a second time, which can cause issues when other plugins expect the version core has but get your plugins version instead ( or when every plugin tries to register its own version )