This looks similar to
Drupal 7 keeps returning to install.php and reports no settings.php but it's all there
but I only just registered so can't comment.
This is a single site (still drupal 7.59). free_access is true, sites/defaults/settings.php is writeable by all (website on local machine to try to figure out solution.) Connection to mysql seems OK.
One clue: if I proceed to install, "Verify requirements" says things like:
The Drupal installer requires that the ./sites/default/default.settings.php file not be modified in any way from the original download.
yet from within the nginx root directory:
# ls -l sites/default/default.settings.php
-rw-r--r-- 1 root users 26250 May 3 15:53 sites/default/default.settings.php
so where does drupal look? (I didn't find a mention of the root directory in the database...)