I think this may be a dupe because I feel like we've discussed it before somewhere, but:
VE is not aware of all categories shown at the bottom of a page, only the categories from the page itself. It doesn't know about all the categories from transclusions. For this reason, I don't think we can *simply* generate a category footer when switching from source, or even accurately update an existing one based on editing through the option dialog (because if you remove from there, it might still be getting the category from a transclusion, so we'd be wrong to remove it from the category footer)

T63921: VisualEditor: Inherited categories not showing up in category dialog on a category page (should show up clearly differentiated)

@Jdforrester-WMF This is not a duplicate of T52239, I've opened a detailed report for the second problem mentioned as T197951.

Nevermind, I believe that these are separate issues.

It seems that the first problem has been resolved:

1. Go to an article with categories on Wikipedia, e.g. this one
2. Click on edit to enter visual editing mode
3. Observe how the categories are displayed at the bottom:
   
4. Click on the categories to open the category editor and add a category, e.g. "Hunde".
5. Save the changes in the category editor to return to editing the page.

One would now expect to see the added category next to the existing categories, and indeed it shows up:

The second problem, however, is still there:

1. Go to an article with categories on Wikipedia, e.g. this one
2. Click on edit to enter visual editing mode
3. Observe how the categories are displayed at the bottom:
   
4. Now, switch to source editing mode by using the pen symbol in the editor's menu bar.
5. Switch back to visual editing by using the pen symbol in the upper right-hand corner of the editor.

One would expect to again see the categories at the bottom, but nothing is there:

The category box is also missing when one starts editing in source mode directly and then switches to visual editing.

In T145268#4307688, @Cirdan wrote:

It seems that the first problem has been resolved:

1. Go to an article with categories on Wikipedia, e.g. this one
2. Click on edit to enter visual editing mode
3. Observe how the categories are displayed at the bottom:
   
4. Click on the categories to open the category editor and add a category, e.g. "Hunde".
5. Save the changes in the category editor to return to editing the page.

One would now expect to see the added category next to the existing categories, and indeed it shows up:

This was resolved in task T151651 (December 2016).

The second problem, however, is still there:

1. Go to an article with categories on Wikipedia, e.g. this one
2. Click on edit to enter visual editing mode
3. Observe how the categories are displayed at the bottom:
   
4. Now, switch to source editing mode by using the pen symbol in the editor's menu bar.
5. Switch back to visual editing by using the pen symbol in the upper right-hand corner of the editor.

One would expect to again see the categories at the bottom, but nothing is there:

The category box is also missing when one starts editing in source mode directly and then switches to visual editing.

This is now filed as task T251398 and should be resolved soon.

Since there are two separate tasks for these two problems, I'm going to close this task.