So I was having a rough time trying to get a multisite setup working, with custom mapped domain names. Where I ended up, while using a .env file, is the below. Some of this I got from another post on the site.
WP_ALLOW_MULTISITE=true
MULTISITE=true
#MU_BASE=
ALLOW_SUBDIRECTORY_INSTALL=false
SUBDOMAIN_INSTALL=true
#DOMAIN_CURRENT_SITE=
PATH_CURRENT_SITE=/
SITE_ID_CURRENT_SITE=1
BLOG_ID_CURRENT_SITE=1
NOBLOGREDIRECT=https://www.example.com
COOKIE_DOMAIN=''
COOKIEPATH=/
SITECOOKIEPATH=/
ADMIN_COOKIE_PATH=/
PLUGINS_COOKIE_PATH=/
I wanted to drop this here in the event that someone else had problems with 403 errors with the wp-json endpoints and returning rest_cookie_invalid_nonce responses.