FreddyFarkleberry

One clue could be the apache <Directory .../> directive applied to the wp-content subdir of the site, but the .htaccess and index.php were in the directory above. Would that matter? (I tested removing the wp-content from the end of the path, but it made no noticable difference.)

Also, wordpress complains about the .htaccess file not being writable. I changed the permissions to 0666 (ownership is www-data.root), but still wordpress complains. (directory is owned by www-data.)

Yes, apache 2.4.10 on debian testing. rewrite module is enabled.
site configuration snippet as follows:

<Directory /path/to/www.dovercottage.com.au/wp-content>
Options FollowSymLinks
AllowOverride All
Require all granted
</Directory>

At top level, i.e. /path/to/www.dovercottage.com.au/, there is a .htaccess file with those exact contents, permissions: 0644.

I didn’t see anything else in that link that would help, but permalinks are still broken. What next?