AFAIK, there is no plugin to accommodate that, and as all links appear to be absolute in Moodle, I have never found a way to automate this process. It's a minor annoyance for me, but I don't have that many courses to deal with.
Thinking about it for a moment, is there another way to archive your courses? For example, all courses are copied to an archive folder, then reset in the present. This would mean that current courses would always be in the "CurrentCourses" Category, with Chemistry > General always in the Current Courses > Chemistry > General category and so on, whereas the archived courses are copied off to Archive>2020-2021 Courses>. There is no 2021-2022 Courses until they are copied off to Archive>2021-2022 Courses > ... The resetting can be done with a predetermined cron job that runs at the appropriate times. this would mean you wouldn't have to update any links, they are all current.
I don't suggest this structure will work, but it might be worth the time testing it in your test site.