I can confirm the issue, but am having trouble pin pointing the issue.

Here's what I know so far:

1. The issue does not occur in Blender 2.82a.
2. The issue occurs in Blender 2.90 with the file provided.
3. However, the issue only occurs with the objects in the file provided. Any new objects added to the scene can be extruded.
4. If I copy one of the objects from the provided file to a new instance of Blender, it can't be edited, lining up with the cause being the objects.

I will continue to investigate to see if I can recreate the issue from a simple file or pin point the cause with the current model.

Yes correct. not matter vertex, edge cause problem on 2.90 I was work and make me frustrate start over, start over many times yesterday and today.

When open Blender 2.90 Alpha there cube is fine extruded.
I got download and clean up everything complete and extrude any edge and/or vertex cause bug of 2.90.

I've found the cause, updating the description to reflect this. I will also bisect the issue to find the commit.

Really good job @Alaska (Alaska)

Note that this isn't related to extrude, drawing any loose wire fails in the file provided, unless all faces are deleted (with only faces option).

Changed the name back. Will start the bisect now unless you know the commit already @Campbell Barton (campbellbarton)

Oh really. Good job. Thank you for fix correct english. My not good english I do know sign language.

I just test what you said very excellent correct answer yaaa ay.

Push the F key is bug while between from vertex to vertex too.

diff --git a/source/blender/draw/intern/draw_cache_extract_mesh.c b/source/blender/draw/intern/draw_cache_extract_mesh.c
index 06462d5b9c5..ff54ab5827e 100644
--- a/source/blender/draw/intern/draw_cache_extract_mesh.c
+++ b/source/blender/draw/intern/draw_cache_extract_mesh.c
@@ -4674,11 +4674,8 @@ static void mesh_render_data_update_task_data_free(MeshRenderDataUpdateTaskData
   MEM_freeN(taskdata);
 }
 
-static void mesh_extract_render_data_node_exec(void *__restrict task_data)
+static void mesh_extract_render_data_node_exec(void *__restrict UNUSED(task_data))
 {
-  MeshRenderDataUpdateTaskData *update_task_data = task_data;
-  mesh_render_data_update(
-      update_task_data->mr, update_task_data->iter_type, update_task_data->data_flag);
 }
 
 static struct TaskNode *mesh_extract_render_data_node_create(struct TaskGraph *task_graph,
@@ -4688,6 +4685,7 @@ static struct TaskNode *mesh_extract_render_data_node_create(struct TaskGraph *t
 {
   MeshRenderDataUpdateTaskData *task_data = MEM_mallocN(sizeof(MeshRenderDataUpdateTaskData),
                                                         __func__);
+  mesh_render_data_update(mr, iter_type, data_flag);
   task_data->mr = mr;
   task_data->iter_type = iter_type;
   task_data->data_flag = data_flag;

Solves the issue. Means that the split of the mesh_render_data isn't working as expected. Will investigate.