There are adapters you can use to work around the lack of wires. The existing wires already include power, it's the ground that's missing.
The existing 4 wires to a standard dumb thermostat are:
Power
heat
A/C
fan
The functions are enabled by connecting power to whichever is required. But there is a missing "C" (common) wire. So, as you discovered, smart thermostats have no easy way to also power themselves.
I was lucky when I added my smart thermostat. It turned out that my 20 y/o house already had an 8 wire cable preinstalled.
For people stuck with 4 wires, there are adapters available that will multiplex two control signals onto one existing wire. This lets you free up another of the existing wires to become the needed fifth C wire.
Here's one setup I found with a quick search. There's even a video. This adapter requires access to both ends, viz. the thermostat and the furnace.
https://smartthermostatguide.com/c-wire-venstar-add-a-wire-a...
This can cause trouble
Ecobee (probably others) provides a Doo-dad that wites into the furnace to help make this work