What has worked for me, I just experienced this last month was in the chat, you need to name the chat something so in the action itself, you can select it from the pick list. So as an example, you have a chat with Alisher and Santosh - create your chat, then click on the "..." and name the chat - some like ChatGroup1 (or anything).
Then you will be able to select it and this will work. Again, I just resolved this in one of my flows last month and those were the steps.
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