Looking for a solution on text management

You can check out textexpander https://textexpander.com/text-expansion or similar tools.

This is one of the things I would love to see too, as an additional feature. Partly this can be achieved by using Incopy, but this is not a drag and drop feature and is only useful with larger text paragraphs (size of a story or column).

On the other hand, as others already pointed out, we'll be probably better off with a dedicated authoring tool.

As mentioned

The CC Library is a place that can store content and added bonus of being shared I would imagine

A normal InDesign Library using File>New>Library and save your Library File

You can drag a story to the desktop or any folder and it creates a Snippet - you can rename the file and store it on your computer in a folder or make available to others through cloud storage. 

There's the Content Collector tool - which for text can also be utilised (I think) as a Place and Link 

Which means the text is copied and placed as a Link in the rest of the text. To change the text in all places you edit the original source the link was created - and then you will see Yellow triangles in the Links panel informing you that the Links are outdated - you can update the Links to update all other text instances throughout the document linked to the single source.

(I've done this for Calendars where you want a miniature Calendar on the back page of the Calendar of each month - Place and Link from the page month and scale it down for the back page - I make an edit on the main calendar and can then update the Link for the back page where there's a minature calendar for each month)

There's plenty of ways to do things - if we know a bit more of what you're trying to accomplish and the problem your facing and the end goal we can direct you to a workflow that suits you.

@ik_9138 

Why? What are you trying to achieve?

Will you be placing the same text multiple times - in different places?

What you're talking about here is, or is close to, what's called Content Management. InDesign doesn't really have any features for storing and managing pieces of content, other than the CC Library feature, which is a bit more oriented towards graphic elements.

I'd suggest that you look into the various "authoring" apps that provide an organized platform for writers, including CMS features for storing text in a managed structure.

InDesign has pretty good "word processing" features but in the end is best used as a final processor for complete material. It doesn't really support the writing/rewriting/organizing processes above an author-managed level.

(Not that, I should add, I think much of "authoring platforms" overall. They strike me as oversold to fledgling authors and unnecessary for anyone who actually has the discipline and ability to write in the first place. But for some projects and fields, the features for managing content as you develop it can be more efficient.)