Understand the tradeoff
In conventional thermostat wiring, Honeywell Home identifies G as fan control and C as common power. Those are different circuit functions. Honeywell Home terminal functions.
The loss of a manual Fan On option does not necessarily mean the furnace blower cannot run during heating. Those functions must be checked separately against the actual equipment's controls. Do not assume cooling airflow or all heating stages (the available heat-output levels) remain correct merely because one heating cycle completed.
Avoid rewiring, bridging terminals, or relabeling more wires based on a diagram for another system. Wire color is not a reliable substitute for tracing the connections and reading the exact instructions.
Compare the supported ways forward
Ask the installer whether the existing cable has a suitable spare conductor, whether a new cable is practical, and whether an approved adapter can retain the functions you want. Ask about the equipment and thermostat combinations each option supports.
For example, Honeywell Home's T10/T10+ installation documentation describes a particular C-wire adapter for certain four-wire heat/cool installations. That is a model-specific solution, not a universal accessory for every two-wire, proprietary, or multi-transformer system. Honeywell Home example adapter application.
Keeping a compatible simpler thermostat can also be a reasonable choice if the added work outweighs the smart features you want. The goal is dependable control with an understood scope, not adding accessories until the display stays on.
Verify the whole control system
Ask for a finished function check covering normal heating, cooling if present, independent fan operation if intended, and any applicable stages or accessories. Have the installer explain any feature you have chosen to give up and record the final setup.
Your next step is to request a correction that preserves the agreed functions using an approved arrangement. State the missing fan function explicitly, so the callback does not end with another screen-power check alone.