On the other hand I also noticed the outdated of my theme but in wordpress it tells me that it has no pending updates.
You’re using a commercial theme. WordPress does not have access to the theme developer’s code to be able to know when new code is available, so WordPress can never tell you there’s new version to install.
Commercial theme vendors handle their own updates and notifications independently.
Some include code in the theme that “phones home” to check if there’s an update. Some bundle a companion plugin to do this. Some only send update notification emails to their customers, and some only maintain a “changelog” page that their customers are supposed to visit regularly to see if theres’ something new.
Anyway, old versions of the theme can influence that way the links do not work?
If you kept everything “old” (ie theme, plugins, server and WordPress), then nothing would break (other than potential security issues).
But once you update one or more parts, changes that have been made in the updated part may not work with the old part that hasn’t been updated, causing the site to break.
For instance, certain PHP code that was valid with PHP 5 may no longer be valid in PHP 7 or 8. Or WordPress may have removed or changed some code in newer versions.
In your specific case, the culprit is likely the outdated jQuery code in the theme: WordPress 5.0 made some major jQuery changes, causing a lot of themes and plugins to break (needing updates). Your theme was updated to become compatible with the new WordPress 5.x, but you’re still running the old code, hence your problem.
It has worked perfectly so the web is already fine and just in case I am not going to update the theme for now.
I’m glad your theme’s author found a quick fix for you.
But I’d consider this only a temporary fix to buy you time to plan and update your theme: sooner or later, another thing is going to break, and before you know it… the entire site is broken.