404 /api/v3/user/login when logging in

Yeah, the config file on the documentation sucks. I had to poke through several discussions on /c/selfhosting to find a config that wasn't the extremely minimal one linked in the documentation. Your config.hjson is fine from what I can tell, although I'm not sure why you censored the hostname there as it's supposed to be lemmy.emphisia.nl and not anything confidential.

Honestly, I don't have enough understanding of NGINX to debug its config, so I'll just share my docker-compose.yml for leddit.danmark.party which worked correctly and federated out of the box, with a few adjustments to match your deployment. Note that you'll have to tear down your existing deployment if you want to use this docker-compose.yml because they use the same ports.

::: spoiler I should probably self-host my own pastebin

version: "3.9"
x-logging:
  &default-logging
  options:
    max-size: '10m'
  driver: json-file

services:
  caddy:
    image: caddy:2
    volumes:
      - ./volumes/caddy:/data
      - ./volumes/caddy:/config
    # See Caddy's documentation for customizing this line
    # https://caddyserver.com/docs/quick-starts/reverse-proxy
    command:
      - /bin/sh
      - -c
      - |
        cat <<EOF > /etc/caddy/Caddyfile && caddy run --config /etc/caddy/Caddyfile
        
        {
          debug
        }
        
        (common) {
        	encode gzip
        	header {
        		-Server
        		Strict-Transport-Security "max-age=31536000; include-subdomains;"
        		X-XSS-Protection "1; mode=block"
        		X-Frame-Options "DENY"
        		X-Content-Type-Options nosniff
        		Referrer-Policy no-referrer-when-downgrade
        		X-Robots-Tag "none"
        	}
        }       
        
        # Lemmy instance
        lemmy.emphisia.nl {
          log
          import common
          reverse_proxy http://lemmy-ui:1234 # lemmy-ui
          
          @lemmy {
        		path /api/*
        		path /pictrs/*
        		path /feeds/*
        		path /nodeinfo/*
        		path /.well-known/*
        	}
         
         	@lemmy-hdr {
        		header Accept application/*
        	}
          
          handle @lemmy {
            reverse_proxy http://lemmy:8085 # lemmy
          }
          
          handle @lemmy-hdr {
            reverse_proxy http://lemmy:8085
          }
          
          @lemmy-post {
        		method POST
        	}
        
        	handle @lemmy-post {
        		reverse_proxy http://lemmy:8085
        	}
        }
        EOF
    lemmy:
      image: dessalines/lemmy:0.18.1-rc.9
      ports:
        - 8085:8536
      volumes:
        - ./lemmy.hjson:/config/config.hjson
      depends_on:
        - postgres
        - pictrs
      restart: always
      logging: *default-logging
      
    lemmy-ui:
      image: dessalines/lemmy-ui:0.18.1-rc.9
      ports:
       - 1234:1234
      environment:
        - LEMMY_UI_LEMMY_INTERNAL_HOST=lemmy:8085
        - LEMMY_UI_LEMMY_EXTERNAL_HOST=localhost:1236
      depends_on:
        - lemmy
      volumes:
        - ./volumes/lemmy-ui/extra_themes:/app/extra_themes
      restart: always
      logging: *default-logging
   
    postgres:
      image: postgres:15-alpine
      ports:
        - 5432:5432
      environment:
        - POSTGRES_USER=MyPostgresUser
        - POSTGRES_DB=MyPostgresDb
        - POSTGRES_PASSWORD=MyPostgresPassword
      volumes:
        - ./volumes/postgres:/var/lib/postgresql/data
      restart: always
      logging: *default-logging
      
    pictrs:
      image: asonix/pictrs:0.4.0-rc.7
      user: 991:991
      hostname: pictrs
      environment:
        - PICTRS__MEDIA__VIDEO_CODEC=vp9
        - PICTRS__MEDIA__GIF__MAX_WIDTH=256
        - PICTRS__MEDIA__GIF__MAX_HEIGHT=256
        - PICTRS__MEDIA__GIF__MAX_AREA=65536
        - PICTRS__MEDIA__GIF__MAX_FRAME_COUNT=400
      volumes:
        - ./volumes/pictrs:/mnt
      restart: always
      logging: *default-logging
	  
    postfix:
      image: mwader/postfix-relay
      environment:
       - POSTFIX_myhostname=lemmy.emphisia.nl
      restart: "always"
      logging: *default-logging

:::