autotutorial

https://support.google.com/webmasters/answer/35179
Yoast Seo set google search console for you, if you have used google Analytics you can set google search console from there. https://yoast.com/wordpress/plugins/seo/add-website-google-search-console/
Yoast Seo add your sitemap if you enable it.

Google search console for analytics https://support.google.com/analytics/answer/1308621
Plugin for Analytics https://wordpress.org/plugins/google-analytics-for-wordpress/

Note* I checked your api rest and it works with the rewriting of the url (mod_rewrite) requirement to create a proper sitemap with Yoast Seo.
Please you can create test.php?

<?php
echo __FILE__;

Set your document root into wp-config.php, first of require_once (copy output of your scrip without /test.php)

$_SERVER['DOCUMENT_ROOT'] = 'output script';
$_ENV['DOCUMENT_ROOT'] = 'output script';

https://wordpress.org/support/topic/fatal-error-wp-settings-php-on-line-162-after-installing-the-last-wp-version/#post-12127727
read the part about the owner or the permissions, if the owner is php you need 775 permissions for the folders and 664 (or 100

https://wordpress.org/support/article/changing-file-permissions/#php5-cgi-permissions

) on the files if the owner is ftp you need 755 and 644 (or 100

https://wordpress.org/support/article/changing-file-permissions/#php5-cgi-permissions

) for the files.
Read all

https://wordpress.org/support/article/changing-file-permissions/

Security in 5.2

simply wordpress does not send any signature.

Still not the right solution, you need to encode nginx from the htaccess file … otherwise you’ll soon have problems with plugins https://wordpress.org/support/article/htaccess/
If you know the syntax of nginx do not copy / paste this article but modofy as it is written in htacces otherwise do copy paste.

Nginx

before explaining what a multusite is, it’s good to learn the terminology to use, with the first WordPress installation you create the first site, only later you can create a network of sites where the first site is called the primary site while all the others are they will call secondary sites. We hypothesized that I created WordPress from domain.tld https://en.m.wikipedia.org/wiki/Second-level_domain and then create the network here I have the first primary site (with id 1 otherwise there are other unexpected events) at this point WordPress puts you two multisite choices with subdirectories (in reality it does not create a directory but is a unique path) or subdomain example Network -> domain.tld
1) with secondary site subdirectory -> domain.tld/ns1
2) or with secondary site subdomain ns1.domain.com

Example secondary site with id 2 (id 1 for primary site) if different it changes in your id http://ns1.domain.tld/wp-admin/network/site-info.php?id=2 (or http://domain.tld/ns1/wp-admin/network/site-info.php?id=2)

in this scenary the Super adminin (owner who installed and subsequently created the network) will have a .domain.tld cookie and then create a cookie on .ns1.domain.tld in the case of installation with subdomain or on domain.tld with subdirectory, means access you have secondary sites without logging in.

From wordpress 4.5 (without WordPress MU Domain Mapping plugins or other plugins) there is the mapping of secondary domains that reference the mapped path or subdomain
Example with subdirectory domain.tld/ns1 (or subdomain ns1.domain.tld) -> any.domain.com
Even if you log in from any.domain.com you will have problems with the cookie because wordpress is requesting to domain.tld/ns1 (or subdomain ns1.domain.tld).
In the first case you can use this define('COOKIE_DOMAIN', $_SERVER['HTTP_HOST']); otherwise define('COOKIE_DOMAIN', '');.
if the primary site and all secondary sites with or without mapping do not have the suffix www. you can dynamically remove these four letters from the variable I provided you and if in the case of domain mapping you cannot set subdomains with domain.tld you can also determine which one is mapped and which is not. Having said that you can also configure your dns for domain.tld and *.domain.tld in the case of mapping ns1.domain.tld will have to point to the mapped domain and with this scenario you don’t need to add other variables to wp-config.php, you have to set DOMAIN_CURRENT_SITE on the primary site (statically not with the variable) I think it serves to identify uniquely to which network it belongs.

Nginx multisite subdirectory

This is the Ningx guide offered by wordpress but you have to rely on the htaccess file (there are different types of versions depending on whether you started with WordPress 3.5 or even earlier).

htaccess

Uploaded File Path #Uploaded File Path
Your first site on a fresh install will put uploaded files in the traditional location of /wp-content/uploads/, however all subsequent sites on your network will be in the /wp-content/uploads/sites/ folder, in their own subfolder based on the site number, designated by the database. These files will be accessible via that URL.

This is a change from Multisite 3.0-3.4.2, where images of subsites were stored in /wp-content/blogs.dir/ and were shown in http://example.com/files/ and http://example.com/sitename/files and so on. If you started with a Multisite install older than 3.5, it is not an error if your images show with the URL of /files/.

I refer you to this discussion to set a default domain (read the whole article is also useful for ssl) if it does not correspond to the wordpress domain redirects to id 1 this case in the case of mismatch).
https://stackoverflow.com/questions/9824328/why-is-nginx-responding-to-any-domain-name
This is an example for per domain and subdomain on ningx (have dense for multisite subdomain), in reality you should exclude the www subdomain if you want to follow the rule I recommended to you.

server {
    server_name domain.tld *.domain.tld;
    [...]
}

If is_front_page is true and is_home is false it is static page without you set as the "Posts page".

If you set a static page for the front page of your site, this function will return true when viewing that page.

Otherwise the same as @see is_home()

otherwise: is_front_page and is_home true it is a static page you set as the "Posts page" or

Depends on the site’s "Front page displays" Reading Settings ‘show_on_front’ and ‘page_on_front’.

sorry I didn’t understand what you wrote but I’ll explain how wordpress works. Install WordPress apply for the multisite and you must add a constant in your wp-config.php from that moment you can choose by subdirectory or subdomain (an htaccess file and other constants will be created in wp-config.php) From wordpress 4.5 (without using WordPress MU Domain Mapping or other plugins) when from the network you edit a secondary domain (I think a new table is created that remembers the new domain from the old path). an example follows network (primary site) domain.tld installation with subdirectory secondary site domain.tld/site1 (with or without http/https) with subdomain site1.domain.tld (you can only create secondary sites that are based on the network in this case added by subdomain site1 and added network domain.tld) domain.tld domain mapping can be any domain you have also chosen a domain without domain.tld example from site1.domain.tld to new.site.com (in this case you should have new.site.com in your database pointing to site1.domain.tld). I believe that the use of the relocate constant has restored your multisite in normal installation (has modified htaccess and wp-config.php) if you can enter your database on phpmyadmin after clicking your database name you can search for tables with prefix wp if you don’t use wp but you have customized your prefix for example word you have to use this last one for the search, the tables wp_x_ (where x is a numerical value represents your secondary site) (to understand if you use subdirectories or subdomains) I don’t know how to indicate the tables for the mapping you will have to arrange yourself. Important do not change manually in your database (in some cases you can install a plugin that does this work for you but first you need to understand what installation it was and maybe backup your files and database). Can you bring me the path of wp_x_? Can you bring back your htaccess? Can you bring me the variables in your wp-config.php? (no password, nothing about the salt or the database but after the constant Multisite) Can you give me the name of the mapping table and the route?