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Unfortunately, I believe this is not possible right now. Having the Text area field in rich text editor mode would mean a highly customizable text field.
I will, however, escalate this to our developers so that they can further check if this can be an added in the fillable PDF form. Unfortunately, we're unable to provide an estimated date for this.
Thanks for heads up. I just implemented necessary changes to put rich text fields into PDF forms, however it is transferred as regular text area because as Charlie already mentioned putting a rich text like in web forms is impossible in PDF.