So on one hand, I finally found out that the busted part of my office chair is called the chair mechanism, so I can finally look for a replacement. On the other, I found out that mine is apparently some super unique size, so I can't actually find a replacement that'll fit. It needs screw-holes that're 13x20 cm apart, but the smallest I can find anywhere is 15x20. So close, yet so far...

@Pink_Hat: https://www.ebay.com/itm/224260909285?chn=ps&mkevt=1&mkcid=28&var=523045577364
Found one that's one cm off. If it doesn't fit a few minutes with a file should be able to open it up enough.
Or you could make a shank with the handle.