Overview
I needed to create IIIF Presentation API v3 manifest files, so I will introduce how to create them using Omeka S.
Installing Omeka S and the IIIF Server Module
Please install by referring to the following resource.
https://zenn.dev/nakamura196/books/f4f87f9730e12e
Creating Items in Omeka S
This time, we will use the following image published by the National Diet Library.
https://dl.ndl.go.jp/api/iiif/2585098/R0000003/full/full/0/default.jpg
Create a new item and give it an appropriate title.

Next, select the “Media” tab, then select “URL” from the menu on the right side of the screen. Enter the image URL in the “URL” field.

Then, click the “Add” button in the upper right corner of the screen to register the item.
IIIF Manifest
This time, I created an item on the site https://omekas.aws.ldas.jp/omeka4/ and the internal Omeka ID 19 was assigned.
v2
With this, the IIIF Presentation API v2 manifest file can be accessed at the following URL.
https://omekas.aws.ldas.jp/omeka4/iiif/19/manifest
Alternatively, you can add the API version /2 and access it at the following URL.
https://omekas.aws.ldas.jp/omeka4/iiif/2/19/manifest
v3
By changing the /2 part above to /3, you can access the IIIF Presentation API v3 manifest file.
https://omekas.aws.ldas.jp/omeka4/iiif/3/19/manifest
Alternatively, by changing the default version to 3 in the IIIF Server module settings screen, the v3 manifest file will be generated when no version is specified.

Summary
I hope this serves as a useful reference for generating IIIF Presentation API v3 (and Image API v3) files.