If the automatic bed leveling routine does not display green for each touch point I recommend printing out and installing shims made of PLA. Positive numbers on the display are high points while negative numbers are low points. By shimming the low points to bring them up to the height of the high points your bed will be more level and your prints more accurate.
Be warned, installing shims is aggravating. The print plate is removed and below it you will see four screws. Those screws go through the heated plate, through spacers, and screw into a bottom mount plate. The spacers are difficult to keep on the screws and lined up with the bottom mounting plate threaded screw holes. On the bright side, anywhere you are placing shims you can screw the shim onto the screw which will keep the shim and spacer on the screw for easy fastening.
Squaring Your Gantry
The next thing to do is use a Speed Square to assess the squareness of the vertical gantry to the top of the Ender printer. The Ender 3 V3 SE is notorious for having a gantry that leans back and is not square to the bed surface.
A gantry that is not square can also be fixed with shims. This is more an issue of trial and error, installing a shim on each side, checking for squareness and either keeping the one you have installed or installing a taller shim or lower shim.
I recommend printing out two of each shim just in case both sides of the gantry need the same thickness shim.
You then unscrew the gantry from the base in the opposite way you put it together in Step 3, install a mid-size shim on both sides, screw the gantry back to the base and test for squareness with the Speed Square.
Repeat this process until you have found this best working gantry shims for your Ender printer.
Move the Filament Spool Holder to the Side of the 3D Printer
Having the weight of the Filament spool on the top of the 3D printer causes increased vibration when the print nozzle is moving around the print bed.
By moving the filament spool holder to the right side of the printer this vibration is reduced.
The mount slides under and up against the bottom edge of the printer base and the left and right holders just clip onto the gantry. You do not need to take apart your printer to attach the clip.
The mount does need to have M5-0.8 threads installed in the mount where the spool holder attaches to it. Any normal metric Tap & Die set will work for this.
With the Filament spool on the side of the printer I recommend using two filament guides that are clipped onto the top gantry bar where the spool holder was to guide the filament into the print nozzle.