It's hard to explain so i'll create an example here:

/execute as @e[type=!player] at @s if entity @p[distance=..1] run say Success

The command at the end will only be executed if all entities (except the player) are 1 block or less away from the player. The following also didn't work, which quite confused me:

/execute as @e[type=!player] at @s run execute if entity @p[distance=..1] run say Success

Increasing the distance so that all entities were in range of me, allowed the command at the end to run