Use PrecompileTools mechanics to compile REPL (#55782)

Fixes #55778

Based on discussion here
#55778 (comment)

With this `?reinterpret` feels instant, with only these precompiles at
the start.
![Screenshot 2024-09-16 at 9 49
39 AM](https://github.com/user-attachments/assets/20dc016d-c6f7-4870-acd7-0e795dcf541b)

stdlib/REPL/src/precompile.jl

@@ -13,7 +13,7 @@ finally
     Base._track_dependencies[] = true
 end
 
-let
+function repl_workload()
     # these are intentionally triggered
     allowed_errors = [
         "BoundsError: attempt to access 0-element Vector{Any} at index [1]",
@@ -175,9 +175,38 @@ let
     nothing
 end
 
-precompile(Tuple{typeof(Base.setindex!), Base.Dict{Any, Any}, Any, Int})
-precompile(Tuple{typeof(Base.delete!), Base.Set{Any}, String})
-precompile(Tuple{typeof(Base.:(==)), Char, String})
-precompile(Tuple{typeof(Base.reseteof), Base.TTY})
+# Copied from PrecompileTools.jl
+let
+    function check_edges(node)
+        parentmi = node.mi_info.mi
+        for child in node.children
+            childmi = child.mi_info.mi
+            if !(isdefined(childmi, :backedges) && parentmi ∈ childmi.backedges)
+                precompile(childmi.specTypes)
+            end
+            check_edges(child)
+        end
+    end
+
+    if Base.generating_output() && Base.JLOptions().use_pkgimages != 0
+        Core.Compiler.Timings.reset_timings()
+        Core.Compiler.__set_measure_typeinf(true)
+        try
+            repl_workload()
+        finally
+            Core.Compiler.__set_measure_typeinf(false)
+            Core.Compiler.Timings.close_current_timer()
+        end
+        roots = Core.Compiler.Timings._timings[1].children
+        for child in roots
+            precompile(child.mi_info.mi.specTypes)
+            check_edges(child)
+        end
+        precompile(Tuple{typeof(Base.setindex!), Base.Dict{Any, Any}, Any, Int})
+        precompile(Tuple{typeof(Base.delete!), Base.Set{Any}, String})
+        precompile(Tuple{typeof(Base.:(==)), Char, String})
+        precompile(Tuple{typeof(Base.reseteof), Base.TTY})
+    end
+end
 
 end # Precompile