NPN Transistors Not Working When Emitter Is Grounded
I solved my own issue by buying different transistors. All 5 PN2222 NPN transistors I got are apparently faulty.

I purchased a small electronics starter kit on Amazon as it was a Prime Day deal and it seemed like a steal at the time. However, the transistors I received were all faulty out-of-the-box.  In addition, some other components included in the kit have been noted to not work here and there (bad quality control, I guess ¯(°_o)/¯ ).

Please learn from my shopping mistake and buy a better kit elsewhere.