Prep. Leave your best armor in a shulker box. Warden negates any damage it may reduce anyways. Wings. Bow. Arrows (top harming arrows if possible, silk touch diamond hoe to fast mine blocks, torches/lanterns to mark safe areas, a couple golden apples if possible, and rockets (ideally duration 1 as you don’t want strong rockets flying in the city. And bring 2 water buckets. Very important. Any enchantments you want but a strong bow and max depth strider.
Strategy. Your main opponent in the deep dark are the shrieker blocks. They are your target. Remove those and you remove the danger of the warden. Use your silk touch hoe on these things. Using your water buckets, create infinite water in a generally safe area. Then put water elevators everywhere. Ideally, build your area of operations on top of the portal. It’s out of reach of warden shots and you have a good vantage point. Put water elevators off all sides for easy access back up top. If the warden is summoned and pops out, use 1 rocket and fly away. Use water to easily break your flight if needed. Stay up high on ledges as you will be out of darkness and range. Wait for the thing to despawn and then continue on.
Make your way throughout using sneak, kill shriekers, look for chests, and mark found chests with lots of torches so you know it’s found.
Profit.