You could also create an edge and use the tiny cad tools to create verts where 2 edges intersect. You might have to fill in some faces, delete a few extra verts and edges, but is precise, especially useful if a new transform axis is created for that edge
On the spot I’d use one of the following wonky workarounds.
A) might be impossible depending on the geometry B) really isn’t as messy as it sounds, C) I’d seldom use.
A)
Edge Slide allows numerical input, and plays well with n-gons and weird non-manifolds. But you’ll have to work the math out from the midpoint.
B)
subdivide the edge once
activate Active Element as Pivot Mode
Select the new vert, then one of the edge end-points
“slide” the vert numerically precise by hitting S, then the number.
I might snap the new vert into one of the endpoints and scale it towards the other, if the more straightforward 0-1 scaling math is worth it.
Also, only selecting new vertices between operations, the value-scaling is repeatable with shift+r.