After the manifest and service workers have been fully configured, the PWA is not displayed.

The PWA Builder was used for testing. After entering the URL, my icon/image and the name of my website with a short name are displayed correctly.
After a few seconds of "testing progress", my logo image and the name of my website disappear and Stela Theme is displayed. The note for action items changes from 1 to 3.

Icons in sizes from 16x16 to 512x512 were uploaded.

In the mobile browser, even after restarting the browser and deleting cookies, there is no note on the screen about installing the PWA.
Also in the  mobile chrome browser, when I add it to my homepage, only Stela is displayed instead of my website name.

1) use https://www.pwabuilder.com/ to review what you miss
2) in chrome, press F12 and on Application tab you also see issues with PWA.

1) use https://www.pwabuilder.com/ to review what you miss
2) in chrome, press F12 and on Application tab you also see issues with PWA.

I have attached a screenshot of the PWA Plugin and PWA Builder configuration.
As you can see in the plugin, the name and short name of the website have been inserted.
However, in the PWA Builder you only see the name of the Stela theme and no logo image. As you can also see, it says that the icon in size 512x512 is missing but this image was also uploaded as a PNG, see my previous post.

Do I have to upload the manifest and the service worker manually to the file manager?

Solve errors.

Solve errors.

There seems to be a misunderstanding in our communication.

I have already clearly stated that I have filled in the required fields and also uploaded the icon in 512x512 in PNG format to the PWA plugin.

I have also given the name and short name of the website.

This is also shown in the manifest.webmanifest, see attachment.

However, the implementation of the PWA does not seem to work.

The PWABuilder does not show my icon or the rest of my site's data.

A photo manifest.webmanifest has been uploaded and you can clearly see that the necessary things have been fulfilled.

Why does the PWABuilder first show a correct summary and then a few seconds later there is nothing to see?

Your problem is in configuration, not in plugin.
Make sure that icon is really 512x512, if it complains it's not there, then it's not there. You also have more details on info button click.
Also make sure you don't have 2 manifest files in header (one from theme and one from PWA as it will read just first).

You can also create manifest in PWAbuilder.com.

The problem was resolved and the plugin works perfectly. It was displayed correctly by the PWABuilder.
There were two manifests in the header.
I deleted them both and generated the manifest from the PWA plugin again. After that it worked.