Impossible d'accéder à l'application Docker à partir du navigateur

J'ai une API .NET Core 2.1 qui, lorsqu'elle est exécutée via Visual Studio dans Windows, reçoit un HTTP GET du navigateur et renvoie avec succès les données d'une base de données MySQL.

J'ai essayé d'ajouter l'API à un conteneur Docker (dans Ubuntu) - cela se construit, mais je ne peux pas accéder à l'API depuis le navigateur:

Ce que j'ai essayé :

• Vérification des ports disponibles. Voici la sortie pertinente:

• Connexion à l'aide d'un autre navigateur: dans Chromium, le message "Ce site ne peut pas être atteint: localhost a fermé la connexion de manière inattendue."
• Testing unused ports in the browser to see if this returns a different message - for Firefox, unused ports return 'Unable to connect' instead of 'Secure connection Failed', and in Chromium they return 'localhost refused to connect.' instead of 'localhost unexpectedly closed the connection.'
• In Firefox, configuring 'security.tls.insecure_fallback_hosts' to 'localhost'.
• Double-checking that ports are mapped correctly in docker-compose.yml - under 'ports' for the relevant container, 44329 is mapped to 44329.
• Running a DB query when the API starts and logging the result: this is successful. I run docker-compose up, the API starts, connects to the DB container, and it logs the result of an SQL query to a text file. So the problem is unlikely to be anything to do with the database.
• Logging GET requests: Inside Windows, the GET requests are successfully logged, but in the Ubuntu Docker container, they're not.

This might be relevant: In Windows, the API only works properly if you start it from Visual Studio. If you execute dotnet webapi.dll, you get this output

...\netcoreapp2.1>dotnet webapi.dll
...
Now listening on: http://localhost:5000
Now listening on: https://localhost:5001
Application started. Press Ctrl+C to shut down.

So here it's not running on 44329; instead it's accessible via 5001 in the browser, where you get this message which is not chill at all: Clicking 'ADVANCED' allows you to continue to the API.

• So I've also tried connecting via 5001 in Ubuntu without luck.

Here's the output from 'docker-compose up':

matt@Matt-Ubuntu:~/docker2$ docker-compose up
Starting docker2_mysql_1 ... done
Starting docker2_dbmodelmapper_1 ... done
Attaching to docker2_mysql_1, docker2_dbmodelmapper_1
... (mysql stuff) ...
dbmodelmapper_1  | Hosting environment: Production
dbmodelmapper_1  | Content root path: /app
dbmodelmapper_1  | Now listening on: http://[::]:80
dbmodelmapper_1  | Application started. Press Ctrl+C to shut down.

• Seeing the port 80, I've tried connecting to that, without success.

• The relevant container as shown by docker ps is:

  

What kind of issue am I looking at here?