Moves additional env vars out of default_env and updates some transient prompt vars (#14579)

# Description

With `NU_LIB_DIRS`, `NU_PLUGIN_DIRS`, and `ENV_CONVERSIONS` now moved
out of `default_env.nu`, we're down to just a few left. This moves all
non-closure `PROMPT` variables out as well (and into Rust `main()`. It
also:

* Implements #14565 and sets the default
`TRANSIENT_PROMPT_COMMAND_RIGHT` and `TRANSIENT_MULTILINE_INDICATOR` to
an empty string so that they are removed for easier copying from the
terminal.
* Reverses portions of #14249 where I was overzealous in some of the
variables that were imported
* Fixes #12096 
* Will be the final fix in place, I believe, to close #13670

# User-Facing Changes

Transient prompt will now remove the right-prompt and
multiline-indicator once a commandline has been entered.

# Tests + Formatting

- 🟢 `toolkit fmt`
- 🟢 `toolkit clippy`
- 🟢 `toolkit test`
- 🟢 `toolkit test stdlib`
- 
# After Submitting

Release notes addition

crates/nu-utils/src/default_files/default_env.nu

@@ -17,11 +17,6 @@ $env.PROMPT_COMMAND = $env.PROMPT_COMMAND? | default {||
     $path_segment | str replace --all (char path_sep) $"($separator_color)(char path_sep)($path_color)"
 }
 
-$env.PROMPT_INDICATOR = $env.PROMPT_INDICATOR? | default "> "
-$env.PROMPT_INDICATOR_VI_NORMAL = $env.PROMPT_INDICATOR_VI_NORMAL? | default "> "
-$env.PROMPT_INDICATOR_VI_INSERT = $env.PROMPT_INDICATOR_VI_INSERT? | default ": "
-$env.PROMPT_MULTILINE_INDICATOR = $env.PROMPT_MULTILINE_INDICATOR? | default "::: "
-
 $env.PROMPT_COMMAND_RIGHT = $env.PROMPT_COMMAND_RIGHT? | default {|| 
     # create a right prompt in magenta with green separators and am/pm underlined
     let time_segment = ([

src/main.rs

@@ -320,9 +320,29 @@ fn main() -> Result<()> {
         "NU_VERSION".to_string(),
         Value::string(env!("CARGO_PKG_VERSION"), Span::unknown()),
     );
-
     // Add SHLVL if interactive
     if engine_state.is_interactive {
+        engine_state.add_env_var("PROMPT_INDICATOR".to_string(), Value::test_string("> "));
+        engine_state.add_env_var(
+            "PROMPT_INDICATOR_VI_NORMAL".to_string(),
+            Value::test_string("> "),
+        );
+        engine_state.add_env_var(
+            "PROMPT_INDICATOR_VI_INSERT".to_string(),
+            Value::test_string(": "),
+        );
+        engine_state.add_env_var(
+            "PROMPT_MULTILINE_INDICATOR".to_string(),
+            Value::test_string("::: "),
+        );
+        engine_state.add_env_var(
+            "TRANSIENT_PROMPT_MULTILINE_INDICATOR".to_string(),
+            Value::test_string(""),
+        );
+        engine_state.add_env_var(
+            "TRANSIENT_PROMPT_COMMAND_RIGHT".to_string(),
+            Value::test_string(""),
+        );
         let mut shlvl = engine_state
             .get_env_var("SHLVL")
             .map(|x| x.as_str().unwrap_or("0").parse::<i64>().unwrap_or(0))