Partial switching of multiple LEDs using shift registers
There are some misunderstandings on how current is computed.

When using an inverting transistor switch, hFE reduces towards 10% of its max value and is usually rated at hFE=10 at Vce=Vce(sat). Thus Rb must be much lower.

CMOS FETS have a high resistance already for each family.  74HC types such as this  can be viewed in the datasheet for the drop voltage on Vdd-Voh, Vol-Vss(0)  @ Iol,Ioh( eg. 4mA) @ 25'C  Although the tolerance is 50%, and increases with low Vdd, consider nominal Rs = 50 Ohms for 5V logic.

concept of  VE ? Ve=0V gnd