Better serialize the git panel (#34622)

Follow-up of https://github.com/zed-industries/zed/pull/29874
Closes https://github.com/zed-industries/zed/issues/34618
Closes https://github.com/zed-industries/zed/issues/34611

Release Notes:

- N/A

crates/git_ui/src/git_panel.rs

@@ -65,6 +65,7 @@ use ui::{
     ScrollbarState, SplitButton, Tooltip, prelude::*,
 };
 use util::{ResultExt, TryFutureExt, maybe};
+use workspace::SERIALIZATION_THROTTLE_TIME;
 
 use workspace::{
     Workspace,
@@ -342,7 +343,7 @@ pub struct GitPanel {
     pending_commit: Option<Task<()>>,
     amend_pending: bool,
     signoff_enabled: bool,
-    pending_serialization: Task<Option<()>>,
+    pending_serialization: Task<()>,
     pub(crate) project: Entity<Project>,
     scroll_handle: UniformListScrollHandle,
     max_width_item_index: Option<usize>,
@@ -518,7 +519,7 @@ impl GitPanel {
                 pending_commit: None,
                 amend_pending: false,
                 signoff_enabled: false,
-                pending_serialization: Task::ready(None),
+                pending_serialization: Task::ready(()),
                 single_staged_entry: None,
                 single_tracked_entry: None,
                 project,
@@ -709,16 +710,24 @@ impl GitPanel {
         let amend_pending = self.amend_pending;
         let signoff_enabled = self.signoff_enabled;
 
-        let Some(serialization_key) = self
+        self.pending_serialization = cx.spawn(async move |git_panel, cx| {
+            cx.background_executor()
+                .timer(SERIALIZATION_THROTTLE_TIME)
+                .await;
+            let Some(serialization_key) = git_panel
+                .update(cx, |git_panel, cx| {
+                    git_panel
                         .workspace
                         .read_with(cx, |workspace, _| Self::serialization_key(workspace))
                         .ok()
                         .flatten()
+                })
+                .ok()
+                .flatten()
             else {
                 return;
             };
-
-        self.pending_serialization = cx.background_spawn(
+            cx.background_spawn(
                 async move {
                     KEY_VALUE_STORE
                         .write_kvp(
@@ -733,7 +742,9 @@ impl GitPanel {
                     anyhow::Ok(())
                 }
                 .log_err(),
-        );
+            )
+            .await;
+        });
     }
 
     pub(crate) fn set_modal_open(&mut self, open: bool, cx: &mut Context<Self>) {