How to add a field to be displayed alongside the title?
Your question may lead to different opinion-based answers. Some might say: Display Suite. Others might say: do it in templates. And you could also: hide this certain field to then preprocess it back as suffix of the title (hook_preprocess_page_title).

All of them are no ideal solutions, IMHO. Display Suite is too heavy. Templates get too fiddly too fast (and I don't like how they can make the Field UI needless). Same for the preprocess function. Although if I would be forced to choose one of the named options I'd rather take the preprocess approach.

What I'd recommend instead is to solve your problem the other way around: Make the title a field, a pseudo field to be precise, that can be placed like any other field in the "Manage display" settings of any content type. Then you simply can drag this title field next to your other field and style them with some basic CSS to be displayed inline.

If you are interested in making the title a pseudo field to solve your problem just implement the code snippets I documented in my other answer on that topic: https://drupal.stackexchange.com/a/263740/15055

Still, if doing it that way you need to edit node.html.twig to remove the default (hard-coded) title output from it, to prevent getting printed twice when viewing this node not as page. Your node title now will be printed like any other field. And of course you also may need to prevent the title block from being printed on your node pages. This can be done per content type in the block settings if I remember it right.