So I made a slightly different solution for you using a sign.
Using this command to give a player a custom sign that places a Redstone torch underneath the door if the player clicking the sign has the admin
tag:
/give @p oak_sign{BlockEntityTag:{Text1:'{"text":"Click to open"}',Text2:'{"text":"door","clickEvent":{"action":"run_command","value":"execute if entity @s[tag=admin] run setblock -63 54 -7 redstone_torch"}}'}} 1
At the end of the command, you can change the position, x y z values, to wherever your door is placed, to place a Redstone torch underneath the door.
This completely hides the opening mechanism underground. And using a few repeaters and a command block to replace the touch with air to close the door.
setblock -63 54 -7 air
I also used an Observer to detect the torch so if someone with admin tag spam clicked the sign the door would not stay open. Like this:

I also placed this command in a repeating command block to teleport any player without the admin tag away from the door:
execute as @a[x=-63,y=56,z=-7,distance=..1] at @s unless entity @s[tag=admin] run tp @s ~0.3 ~ ~
I found that 0.3 was a good amount, at 0.2 you can sprint thru it. And make sure the y position is at feet level, y=56
if it's at the head level it doesn't affect any player walking thru the door.
I also made a quick demonstration video: