I received a response from Metro Vancouver to my inquiry about their "No Public Access" signage.

"The sign you noticed going towards Maquabeak Park references property outside of ƛ̓éxətəm Regional Park. That section is not a Metro Vancouver property, including the trail to Maquabeak Park. I can’t speak to if that trail is open or closed."

I will follow-up with Metro Vancouver and ask that they check with the adjacent land owner (Provincial Health Services Authority) to determine the access provisions and modify their signage if access is allowed.