well:
arduino [1]: 1.38$
nrf [2]: 0.55$
oled [3]: 2.33$
------------------
total: 4.26$
like you said the passive components are pretty cheap, and you stay under 5$.
[1] https://www.aliexpress.com/item/EYEWINK-1pcs-lot-ATMEGA328P-... [2] https://www.aliexpress.com/item/LCD-Board-T420XW01-V2-06A39-... [3] https://www.aliexpress.com/item/Free-Shipping-Blue-0-96-inch...