That piece of drain pipe with **two** hose barbs looks like it was home-made.  Don't try to fix or replace it.

There are lots of similar ones you can buy that will connect **one** hose from a dishwasher or filter like yours.  I suggest you disconnect the *entire* assembly between these two marked points:
 
[![enter image description here][1]][1]


take it whole to a good hardware or plumbing supply store and try to assemble something using products off the shelf that includes two standard dishwasher connections and also assembles so it will match the two existing end points.

While it is disassembled you should place a sandwich bag with a rubber band over the pipe coming out of the wall to avoid smells coming out of it.

There are also some pieces available that will allow you to connect both hoses.  If your store has one, try to make it fit.  Some of these join them together and then exit with a similarly small hose.  I don't know if that's ok for your filter, you need to find out.

[![enter image description here][3]][3]
[![enter image description here][4]][4]
[![enter image description here][5]][5]


  [1]: https://i.sstatic.net/LsAye.png
  [2]: https://www.amazon.com/ET116-001-Adapter-Connect-Fitting-Dishwasher/dp/B08YP9VKHZ/ref=asc_df_B08YP9VKHZ
  [3]: https://i.sstatic.net/OVnMV.png
  [4]: https://i.sstatic.net/qUunn.png
  [5]: https://i.sstatic.net/zdHPW.png