Public Speaking is indeed a soft skill.
There are others -
Let's not neglect the other soft skills critical for now, in 2023 and later :
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Which one are they ?
...
✅ - Effective communication
✅ - Teamwork
✅ - Influencing without authority (softly)
✅ - Problem solving
✅ - Leadership
(Source: The Harvard Business Publishing - Feb. 2023)
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In any listing, whatever the source, communication is key.