To progress through the level, you must use the orange lifts and time your jumps correctly. This can be tricky, so take your time and be patient. Once inside the open level, drop down to the next level and repeat the process.
Finally, reach the blue lift and solve three junction box puzzles to remove barriers blocking your way. This is where things get challenging, so it's important to stay focused and keep your wits about you. Once you've solved the puzzles, you'll be able to progress further into the level.
At this point, you'll need to defeat SHODAN's machine and search it for another mission. This is no easy feat, but with some skill and determination, you'll be able to emerge victorious.
If you prefer a different route to find Anna, you can also turn left at the second left and turn right at the 'Gray' sign. This will take you to the recycling machine room, where you can take the elevator to the Flight Deck. Once you've completed the junction box puzzle to power the bridge, cross it and turn right from the door. Follow the corridor until you reach the end, then drop down to the sub-level.
Alternatively, you can continue around the corridor to find the medical spawn point. Once you receive a call from Anna, drop down to the central blue lift on the floor. From there, you can follow the steps outlined above to find her.