Under Community Review

This idea is under review and may stay like this for a while.  The DeepL API does not support this feature so it's not available anywhere other than their own web interface. This article confirms: https://support.deepl.com/hc/en-us/articles/4407359201938-Selecting-alternative-translations and this part is relevant:

"Alternative translations are not available for the translation of whole documents or supported via the DeepL API/CAT tool access."

[DeepL Translation Provider app] Drop-down menu of alternative translations and dynamic change of whole translation from within Trados Studio

When you click or edit a word in a translation provided in the DeepL web interface (https://www.deepl.com/translator), alternative translations of the selected/edited word are suggested in a drop-down menu as shown in the image below. And when you choose an option from the drop-down, the syntax of the whole translation dynamically changes in some cases (for example, when the subject and object are switched). It would be useful if the same feature can be used from within Trados Studio through the DeepL Translation Provider app.

DeepL web interface showing a translation with a selected word 'dynamic' and a drop-down menu suggesting alternative translations.