Print fallback REPL prompt before user input (#58210)

Using the fallback REPL interactively prints the prompt only after user
input, making the scrollback confusing:
```
$ JULIA_FALLBACK_REPL=1 julia          
1 + 2
julia> 3
```

---------

Co-authored-by: Jameson Nash <vtjnash@gmail.com>
Co-authored-by: Dilum Aluthge <dilum@aluthge.com>

Author: 3 people

base/client.jl

@@ -442,11 +442,12 @@ function run_fallback_repl(interactive::Bool)
                 eval_user_input(stderr, ex, true)
             end
         else
-            while !eof(input)
+            while true
                 if interactive
                     print("julia> ")
                     flush(stdout)
                 end
+                eof(input) && break
                 try
                     line = ""
                     ex = nothing