After updating from drupal 6 to 7: No content types under node/add
I finally managed to fix this by accident while trying to fix a different issue.

Following this post: https://drupal.stackexchange.com/a/82222/25238 
Similar to https://www.drupal.org/node/997444

I first tried drush eval 'menu_rebuild();' drush cc menu which didn't have an effect, then I found the hint in a comment by nilsun to the above post, that sometimes a complete reset might be necessary. This seems to be caused by a corrupt menu system.

$drush sqlc
Password for user user:
psql (8.4.20)
Type "help" for help.
## if you want to try to keep your own menus you could
## first try:

DELETE FROM menu_links WHERE module = 'system'; 
# edit: typo, it's module, not menu
## Tested, did keep my custom menus 

## D_ELETE FROM menu_links # Don't this will delete your custom menus too!
DELETE 748
d7=# DELETE FROM menu_router;
DELETE 909
d7=# \q
$ drush updb
No database updates required                                                          [success]
'all' cache was cleared.                                                              [success]
Finished performing updates.                                                          [ok]
$ drush cc menu
'menu' cache was cleared.                                                             [success]
$ drush eval 'menu_rebuild();'
$ drush cc menu
'menu' cache was cleared.                                                             [success]


Maybe one or two steps can be omitted, but that brought back the content types under "Add content", Edit Warning: while some of my self defined menu entries disappeared, but this should be easy to fix editing them manually.