Use read-only access methods for read-only entity operations (#31479)

Another follow-up to #31254

Release Notes:

- N/A

crates/terminal_view/src/terminal_panel.rs

@@ -702,7 +702,7 @@ impl TerminalPanel {
                 terminal_panel.pending_terminals_to_add += 1;
                 terminal_panel.active_pane.clone()
             })?;
-            let project = workspace.update(cx, |workspace, _| workspace.project().clone())?;
+            let project = workspace.read_with(cx, |workspace, _| workspace.project().clone())?;
             let window_handle = cx.window_handle();
             let terminal = project
                 .update(cx, |project, cx| {
@@ -754,7 +754,7 @@ impl TerminalPanel {
         let width = self.width;
         let Some(serialization_key) = self
             .workspace
-            .update(cx, |workspace, _| {
+            .read_with(cx, |workspace, _| {
                 TerminalPanel::serialization_key(workspace)
             })
             .ok()
@@ -972,7 +972,7 @@ pub fn new_terminal_pane(
             if let Some(tab) = dragged_item.downcast_ref::<DraggedTab>() {
                 let is_current_pane = tab.pane == cx.entity();
                 let Some(can_drag_away) = split_closure_terminal_panel
-                    .update(cx, |terminal_panel, _| {
+                    .read_with(cx, |terminal_panel, _| {
                         let current_panes = terminal_panel.center.panes();
                         !current_panes.contains(&&tab.pane)
                             || current_panes.len() > 1

crates/terminal_view/src/terminal_view.rs

@@ -389,11 +389,9 @@ impl TerminalView {
     fn rerun_task(&mut self, _: &RerunTask, window: &mut Window, cx: &mut Context<Self>) {
         let task = self
             .terminal
-            .update(cx, |terminal, _| {
-                terminal
-                    .task()
-                    .map(|task| terminal_rerun_override(&task.id))
-            })
+            .read(cx)
+            .task()
+            .map(|task| terminal_rerun_override(&task.id))
             .unwrap_or_default();
         window.dispatch_action(Box::new(task), cx);
     }