Stop your server and create a backup, just in case the update fails.
Delete the old server software JAR file (usually named server.jar, double-check your startup command to make sure).
Place the new JAR file in the same directory as the old one. Ensure the name of the JAR is the same, if it has changed, make sure the startup command reflects the change.
Start your server, and run /version or /about to ensure the server is running the new version.
Head to the Startup tab and ensure the version is set to Latest.
Click the Reinstall button. This button overwrites the server.jar file with the latest version of the server software you are using.
Start your server, and run /version or /about to ensure the server is running the new version.
The automatic update system only upgrades your server version (e.g., from 1.20 to 1.21) without changing the server software (e.g., Paper to Forge). To switch server software, please perform a manual update or open a support ticket.