UI: more easily select group for a node

Problem statement

I tried to show a block (Group operations) which would help me assign a newly created node to a group - using the regular drupal functionality.

But:
As an Admin or person who is assigned to multiple groups it is "work" to create a group node:
You have to open the groups list, click through the groups list, select the appropriate group. Go to group content, select to add group content, select which group content, ... to just add a node.

Desired functionality:
I would like to add content the normal drupal way: menu/add content.
Once on the node edit page of the new node (under node/add/*) I would expect a block that shows me the groups I am allowed to add content to. I simply select the group and I would be done!
I tried to place a block (Group operations), but it is not displayed on the form edit page.

Proposed resolution

Use the Entity Group Field contrib module.

See also #2772975-22: Adding node to Group from regular node creation form (/node/add/article, for instance) and #2813405: Add a field to view and edit content's groups.