While the post you reference has an answer, saying that you could speak using your reaction, the RAW say nothing about being able to speak out of turn, while performing a separate readied action. However, the SRD states:
You can communicate however you are able, through brief utterances and gestures, as you take your turn.
In RAW if and only if your reaction occurs on your turn could you speak in character and perform an action, but this seems to be a stiff interpretation of the RAI. It seems likely that because your character is acting in that moment that they could also speak a short phrase in whatever time that specific reaction gives them. As a DM in a situation where intra-party communication was critical 1 or 2 words seems perfectly reasonable for a reaction.
Narratively, if your character was waiting at a corner to strike the first person they saw coming around it, they would not be magically gagged while attacking.