That probably depends on your definition of "woke"
Yes, it was always addressing controversial subjects, was progressive and diverse and inclusive. From a black woman on bridge to low-gravity wheelchair-Arielle in DS9. If that was "woke", it was an inspired wokeness that the viewer had to grapple with, challenge his own prejudices.(*)
What happend to that? Today's "wokeness" feels like a producer mandated LHGBT-Quota, a checkbox to fill during casting, or a right-in-your-face lecture. Again, not because anyone is invested in showing mankind a way to progress, but to please and appease some lobby or viewer target group.
Old Trek never FORCED those "woke" subjects on you. It used to tell great stories, that sometimes were about those subjects. And sometimes it was "monster of the week". But that variety worked. Today, it feels the other way round. "We need to fill those checkboxes. Let's engineer a story around them. By commitee." (**)
Whatever Star Trek always was - woke or not - it's something different today.
Orville has that spirit now, progressing from dick jokes to "Twice in a lifetime"
(*) granted. there were better and worse takes at that. TNG:Justice anyone?
(**) or vice versa. "People notice our checkbox-driven writing. We need to insert some tactical goofiness. Let's do Muppets!"