There are lots of different roles within publishing that all have the word "editor" in the title (Desk Editor, Copy Editor, Development Editor, Production Editor, Commissioning Editor etc), and obviously lots of different avenues that require these services (books, newspapers, magazines, journals, medical/legal documents, websites, marketing etc) so lots of options and opportunities.
I work in book publishing and, in brief, commissioning editors find writers and deal with contracts etc., Development editors then chase those writers until they've written whatever was commissioned. The production editor then oversees the next few stages; the manuscript is then sent to a copyeditor who fixes spellings/grammar etc and makes sure any figures/tables/illustrations are in the right place, correctly labelled and referenced. The manuscript is then typeset and then the pages are reviewed by a proof reader for the final checks. Depending on the type of book, the manuscript may also go to an indexer, which you may also consider looking into... The production editor checks proofs, but would have other responsibilities too such as coordinating the copyeditors, proofreaders, indexers, arranging the cover design, deciding on print run etc.
The sort of work you are describing could be that of a proof reader, copyeditor or production editor. Newspapers/magazines may require faster turnaround, so it might be worth looking into books, journals or marketing collateral which have a slightly longer window in the first instance (just until you get a bit more used to it).
FWIW, I have worked in publishing (books) for a decade and have no editing qualifications. It is possible to get a degree in publishing if you wish, but most people I know have come into it from other routes. Perhaps you could look into shorter courses to begin with (I have heard good things about Chapterhouse Publishing, and I think these courses include ways to find freelance work) This should help you get a bit of exposure/experience to things and see if it is something you'd like to pursue. You could also join LinkedIn and connect with people with the job title "Production Editor" and message to see if they need any freelancers or if they'd be willing to have a chat /discuss what their needs are.
Good luck! 🍀