Next time if something happens like this ...use a CLR solution. I watched your video and it felt like a pain to solve the puzzle of opening and assembling back. Then I found another video where the guy uses CLR. I thought of trying CLR first and it worked for me. But I have to appreciate your patience to open this machine. Thanks for the video.
CLR will not help this problem. Dust, hair, and fine debris block the filter and prevent water flow. Only HF or H2SO4 will dissolve that. If you use those acids however, you will likely hurt yourself or dissolve your steamer. Disassembly is the only option.