How to fix ripped out ball joint in indirect under seat steering recumbent
What you have there is a ball joint (sometimes called a tie rod end)  on a push rod (or track or tie rod) for indirect steering.

I'm astonished it could pop out that easily - Normally they're very secure.

Here's what a car one looks like when exploded.  Yours will be similar but much smaller and lighter.



I think you need a replacement ball joint. These are the same as ones used in car steering systems, and they are unserviceable. You generally cannot disassemble them without destroying the seal - all you can do is grease them via a grease nipple, if they have one.

The old parts should unscrew from the track rod end (there may be a clamp or retainer screw) and from the fork's arm. On a car, you use a Ball Joint Splitter to get the ball part out of the arm. The hole has sloped sides for an inference fit once tight, just like the sides of a square taper are sloped. In the exploded pic above, the slopey sided bit is clearly visible between the ball and the threadded part.  Yours will likely be too small for a car tool.

This is a Ball joint fork - hammered in.


And this is a ball joint separator which levers the ball out.