Suggestion on using a switch across 5V pin of ESP32 SIM800L

I am trying to build a Eink display that updates sensor values once every 5 minutes.

I want the system to be ultra low power. So, I put it to deep sleep every 5 minutes in the day and also during the entire night when it is not reading.

Here are the omponents I used.
ESP32 SIM800L.(LILYGO TTGO T-Call ESP32 SIM800L)
IT8951 Driver Hat.
Waveshare 9.3 Inch Eink Display.
Sensor that works on 3.3V.

I got the system working. The driver itself uses around 110mA when updating and uses around 80mA when idle.

I had to use the 5V pin for the IT8951. So, it draws around 80mA even when the ESP32 is in deep sleep. Even if I put the IT8951 to sleep it draws around 15mA which is a lot over time because I am running it on batteries.

Q1) So, I need advice on is it is good idea to have a switch between the 5V pin and the IT8951 driver.

Q2) Can I draw 120mA without damaging the 5Vpin.

Q3) From the list below can you suggest me the best kind of switch that consumes low power, lasts long and serves the purpose.
a) A suitable 3V Relay.
b) Bipolar Junction Transistor like 2F222(or any suggestions)
c) MOSFET such as the IRF520 module.(or any suggestions)

Thanks in advance.

My preference would be the MOSFET, it is a voltage rather then a current controlled device. Be sure you have no LEDs illuminated when sleeping.