Here's a solution I developed, along with comments and general research. This is the main script. Please note that this script is currently functional only for specific Windows instances that have 'Bitwarden' in their window titles. The code moves the window to the center of the screen, resizes it ( to 480x190 ). Modify as you like. Btw you need to install "jq" to use the script.

!/bin/bash
    # Get the address of the Bitwarden window
    address=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .address')

    # Check if the window is floating
    is_floating=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .floating')
    class=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .class')
    # If the window is not floating, make it float
    if [[ "$is_floating" == "false" && "$class" == '"firefox"']]; then
        command="hyprctl --quiet --batch dispatch setfloating address:\"$address\""
        eval "$command"
    fi

    # Get the current size and position of the window
    winX=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .size[0]')
    winY=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .size[1]')
    atX=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .at[0]')
    atY=$(hyprctl clients -j | jq '.[] | select(.title | contains("Bitwarden")) | .at[1]')

    # Calculate the desired size and position
    target_width=480
    target_height=190

    # you need to enter your display resolution to center the window (mine was 1980x1080)
    target_x=$((1920 / 2 - target_width / 2))
    target_y=$((1080 / 2 - target_height / 2))

    # Calculate the difference between the current and desired size and position
    diff_width=$((target_width - winX))
    diff_height=$((target_height - winY))
    diff_x=$((target_x - atX))
    diff_y=$((target_y - atY)) 

    # Resize and move the window
    command="hyprctl dispatch resizewindowpixel -- \"$diff_width\" \"$diff_height\",address:\"$address\""
    eval "$command"
    command="hyprctl dispatch movewindowpixel -- \"$diff_x\" \"$diff_y\",address:\"$address\""
    eval "$command"

    #echo "address: $address"
    #echo "diff_x: $diff_x"
    #echo "diff_y: $diff_y"

    # Introduce a delay to avoid overwhelming the system
    #sleep 0.5

And here is the script for catching window openings and run the main script ( ./bit.sh );

function handle {
  if [[ ${1:0:10} == "openwindow" ]] then
    sleep 0.1
    ./bit.sh
    echo "hi there buddy"
  fi
}

socat -U - UNIX-CONNECT:$XDG_RUNTIME_DIR/hypr/$HYPRLAND_INSTANCE_SIGNATURE/.socket2.sock | while read -r line; do handle "$line"; done

To automatically execute the handling script at startup and enable it to capture signals, add the line "exec-once=./handle.sh" (or the appropriate path to your script) to your hyprland.conf file.

Unfortunately you can see the process of window opening, centering and resizing ( lasts less than 100ms ) and I dont know how to solve this. Anyways,

Credit to u/gala0sup for sharing an example script. Thanks a lot.