refactor(terminal): cleanup deprecated flush logic (#6373)

Removes flush logic that was leftover to test against ratatui's flush
Cleaned up the flush logic so it's a bit more intent revealing.
DrawCommand now owns the Cells that it draws as this works around a
borrow checker problem.

codex-rs/Cargo.lock

@@ -1455,6 +1455,7 @@ dependencies = [
  "codex-windows-sandbox",
  "color-eyre",
  "crossterm",
+ "derive_more 2.0.1",
  "diffy",
  "dirs",
  "dunce",
@@ -1658,6 +1659,15 @@ dependencies = [
  "unicode-segmentation",
 ]
 
+[[package]]
+name = "convert_case"
+version = "0.7.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bb402b8d4c85569410425650ce3eddc7d698ed96d39a73f941b08fb63082f1e7"
+dependencies = [
+ "unicode-segmentation",
+]
+
 [[package]]
 name = "core-foundation"
 version = "0.9.4"
@@ -2003,7 +2013,7 @@ version = "1.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "cb7330aeadfbe296029522e6c40f315320aba36fc43a5b3632f3795348f3bd22"
 dependencies = [
- "convert_case",
+ "convert_case 0.6.0",
  "proc-macro2",
  "quote",
  "syn 2.0.104",
@@ -2016,6 +2026,7 @@ version = "2.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "bda628edc44c4bb645fbe0f758797143e4e07926f7ebf4e9bdfbd3d2ce621df3"
 dependencies = [
+ "convert_case 0.7.1",
  "proc-macro2",
  "quote",
  "syn 2.0.104",