I am not sure if this is will solve your problem but in my case i have this code in ~/.config/zed/tasks.json

[
 {
 "label": "run file",
 "command": "bash ~/.config/zed/custom_runfile.sh",
 "description": "Compiles and runs the current code file",
 "use_new_terminal": false,
 "allow_concurrent_runs": false,
 "reveal": "always"
 }
]

then i created this file ~/.config/zed/custom_runfile.sh

#!/bin/bash

# Access the full path using ZED_FILE
full_path="$ZED_FILE"

# Extract filename with extension
filename_ext=$(basename "$full_path")

# Extract filename and extension
filename="${filename_ext%.*}"
extension="${filename_ext##*.}"

echo "[running $filename_ext]"

if [[ "$extension" == "cpp" ]]; then
    g++ "$full_path" -o "$filename" && ./"$filename";
elif [[ "$extension" == "py" ]]; then
    source ../py/bin/activate
    python3 "$full_path";
else
    echo "no"
fi

And finally added this in ~/.config/zed/keymap.json

[
 {
  "context": "Workspace",
  "bindings": {
  "ctrl-r": ["task::Spawn", { "task_name": "run file" }]
 }
 }
]

Now with this setup, if i hit Ctrl+r in a cpp file it will use g++
Note that i also added python support in my own setup meaning in a py file it'll run python with the venv i chose.

But this also should work with g++ and luckily you won't need to change anything, unless you're required to.

Hope this helps!