I'm use TMSFNCleaflet maps component and add

Why doesn't the entire map have HERE restrictions? Why do some of the restrictions disappear when I enlarge the screen?
Is it possible to use the newer library here v3?

When using AddTileLayer the custom map layer is placed on top of the default map layer. If specific parts of the custom layer can't be loaded correctly, these are filled with map parts of the underlying default layer.
This seems to be a limitation or issue with the custom layer provider that is unable to provide the necessary map tiles.

While testing this, I noticed the tileserver requests contain "Too many requests" errors.

You can check this yourself, to see if you are getting the same error, by opening the Dev Tools (F12) window and selecting the Network tab. If so, I would suggest to contact the tileserver provider for further assistance.

Hello - thanks for your answer.

Is it possible to somehow query the website again only for the missing data? Is it possible to set some condition in which, after an error occurred, a fragment of the data could be read again, e.g. after waiting 100 ms?

Please note that we only provide the base URL that can be used to request the map tiles, it its the map service provider (in this case Leaflet) that actually controls how and when the requests are made. Unfortunately we have no control over the requests initiated by the map service provider (in this case Leaflet).
This seems to be a limitation or issue of the tileserver provider (in this case Here) that is unable to fulfill all necessary requests.