Thanks for the report.

Considering this feature request and marking as Untriaged.
Requesting Dev team to check the request and update accordingly.

BTW, I also found out it is actually impossible to copy a console log output of an object. Selecting Copy from context menu seems to copy the word "Object" only, highlighting a text range is impossible as the range disappears shortly after the mouseup. This is at least the state of things on Mac.

Maybe you could look into the Copy feature and fix the above...

The bug you mentioned in #4 with being unable to select + copy/paste is being tracked in another issue.  I have an idea of a fix for that:
 crbug.com/674739 

To the original point of the issue, I'm not exactly sure how feasible it will be to paste styled content into Slack.  After reading Slack's docs, it looks like they support a simple markdown language with bold, italic, code, but not things like font, color, background color unfortunately.
https://api.slack.com/docs/message-formatting
https://get.slack.help/hc/en-us/articles/202288908-How-can-I-add-formatting-to-my-messages-

Perhaps there's some documentation that I've missed?  If you know of a way, please let us know!  Otherwise, I don't see how DevTools can prepare content that Slack will style.  Still, a DevTools extension for Slack integration would be neat!  I think there's opportunity for better ways to share console log data.

Frankly, I don't know of any method to integrate with Slack, although I can ask around. However, I wouldn't like the Slack issue to be the main focus for this thicket.

I think there should be a way to copy styled content that could then be recognized upon paste in rich text editors, such as Word or Google mail (is it HTML data behind the scenes?). I sometimes have a need to quote a console error in documentation/manual docs. I thought it'd be easier to copy/drag'n'drop rather than paste in screenshots. If there's too much fuss trying to provide support for this feature in DevTools then feel free to close the ticket.

Ah, okay.  As I understand it, you need to provide some preview of a console error in a document, and today's copy/paste only writes plain text without the rich styling from cases like these:
1) Formatters, e.g. console.log('%cfoo', 'color: blue')
2) The red styled text in errors, e.g. console.error('foo')

The first case should be possible since the color and other styles are directly set on the elements shown.  The second case, however, will not be straightforward since the red color comes from a stylesheet much higher up.

If there's desire for these use cases, let's keep this open.  Thanks for the feature request!

Well, the console output is not alwyas authored by me in js. Often times it's HTTP errors, like OPTIONS preflight or 40x, sometimes it's an error or warning from third-party libraries, so in practice this is not alwyas possible to assume that colors have been applied to text on a certain internal level.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/80f526543bbe0692624591c0f9ef968fec1d498f

commit 80f526543bbe0692624591c0f9ef968fec1d498f
Author: Erik Luo <luoe@chromium.org>
Date: Sat Nov 18 03:37:31 2017

DevTools: allow copying visible text with styles in console

Console's custom copy handler tries to determine the selected text on
its own. In some cases, the browser's default copy handler offers much
better behavior:
- Include styles and colors
- Include table indentation that can be pasted into spreadsheet editors
- Account for text selections across shadow boundaries

Bug:  673746 ,  697149 ,  649828 
Change-Id: I4b5e3a225234e28fe84197a73f655af9c4c9f418
Reviewed-on: https://chromium-review.googlesource.com/773462
Commit-Queue: Erik Luo <luoe@chromium.org>
Reviewed-by: Dmitry Gozman <dgozman@chromium.org>
Cr-Commit-Position: refs/heads/master@{#517691}
[modify] https://crrev.com/80f526543bbe0692624591c0f9ef968fec1d498f/third_party/WebKit/Source/devtools/front_end/console/ConsoleView.js
[modify] https://crrev.com/80f526543bbe0692624591c0f9ef968fec1d498f/third_party/WebKit/Source/devtools/front_end/console/ConsoleViewport.js

To update this bug: we can offer a partial solution for now, in which users "Copy visible styled text" from the right-click context menu to achieve this functionality.  Performing this right click action should allow you to copy text with color, background color, and font from the console.

While a right click option is not as ideal as I'd like, I'm marking this as fixed, since there are no plans in which we could support this without incurring significant complexity.