To open the purple seal doors in Chapter 3 of Black Myth: Wukong, you need to defeat the optional boss Captain Lotus-Vision. Here is a detailed step-by-step process to help you through:

Step 1: Reach the Lower Pagoda Keeper’s Shrine
1. Start from Your Cell: Begin by leaving your cell and heading straight. You will encounter enemies; use Cloud Step to distract them if necessary.
2. Follow the Ledge: Continue along the ledge, avoiding any open doors until you reach the Lower Pagoda Keeper’s Shrine.
3. Explore the Shrine Area: From the Lower Pagoda Keeper’s Shrine, go left and make a sharp right. Keep going straight until you see a dead-end. Instead of going back, head outside using the open door.

Step 2: Navigate to the Upper Pagoda Keeper’s Shrine
1. Climb the Stairs: Move ahead and stop at the lantern with the halfway open gate. Go in and climb up the stairs.
2. Cross the Wooden Beam: Once you reach the top, go right and defeat any enemies that may trouble you. Cross the wooden beam, using Cloud Step to avoid the archer if necessary.
3. Reach the Upper Pagoda Keeper’s Shrine: Take a right, then a left, and keep walking until you see an enemy near a slope. Run up the slope and go past another enemy to reach the Upper Pagoda Keeper’s Shrine.

Step 3: Activate the Shrine and Prepare for the Boss Fight
1. Activate the Shrine: Activate the Upper Pagoda Keeper’s Shrine and save your progress.
2. Prepare for Captain Lotus-Vision: Go back inside and look down to the right where there are lots of stone figurines. Carefully jump down to trigger a fight with Captain Lotus-Vision, a Yaoguai chief.

Step 4: Defeat Captain Lotus-Vision
1. Engage in Combat: Captain Lotus-Vision specializes in long-range attacks, so it is better to get close. Use various spells to make the fight easier. When he launches projectiles, use the staff spin to block them. Be careful of the laser beams, as they deal a lot of damage and cannot be blocked by the staff.
2. Defeat the Boss: With enough upgrades, players should be able to beat Captain Lotus-Vision quickly. After defeating the boss, take its spirit.

Step 5: Unlock the Purple Seal Doors
1. Capture the Spirit: After defeating Captain Lotus-Vision, you will receive his spirit. This spirit will automatically unlock all the purple seal doors in the Pagoda Realm, including the one that holds a prisoner.

By following these steps, you will be able to open the purple seal doors in Chapter 3 of Black Myth: Wukong and access the hidden areas and rewards behind them.