This broader meaning refers to moving slowly through something that resists or obstructs progress.
They waded through deep snow.
He waded through the crowded station.
This figurative meaning refers to reading, examining, or processing something long, complicated, or tedious.
She waded through hundreds of emails.
The lawyer waded through the evidence.
Usually used as wade in or wade into, this meaning refers to entering an argument, dispute, or action energetically.
The politician waded into the debate.
She waded in to defend her colleague.