Overview
I tried Wagtail, so here are my notes on issues I encountered.
I basically followed this tutorial:
https://docs.wagtail.org/en/v5.0.1/getting_started/tutorial.html
Search Function
When I added a page with a Japanese title of “My First Article” (はじめての記事), the following search did not return any results.
http://localhost:8000/admin/pages/search/?q=はじめて
On the other hand, the following search did return results. It seems that partial matching for Japanese is not supported by default.
http://localhost:8000/admin/pages/search/?q=はじめての記事
Wagtail API
The API documentation was found at:
https://docs.wagtail.org/en/v5.0.1/advanced_topics/api/index.html
By also adding rest_framework as described on the above site, I was able to obtain results as shown below.

However, for the app running on localhost:8000, the hostname in the returned results was showing as localhost.
This issue was resolved by modifying it from the admin panel, as described in the following article:
https://stackoverflow.com/questions/52540254/edit-approved-email-points-to-localhost
Specifically, I changed the port number on the /admin/sites/ page.

?search Parameter
Similar to the search function mentioned earlier, Japanese text required an exact match.
http://localhost:8000/api/v2/pages/?search=はじめての記事
Elasticsearch
I tried integrating with Elasticsearch.
https://docs.wagtail.org/en/v5.0.1/topics/search/backends.html
This time I tried AWS OpenSearch, but encountered the following error.
A similar issue has been raised at the following, but it appeared to be unsupported at the time.
https://github.com/wagtail/wagtail/issues/7920
Summary
Some information may be inaccurate, but I hope this serves as a useful reference when using Wagtail.