The heat from the incandescent bulbs is what peels the green paint off the glass. It also burns the paper reflectors behind the bulbs. (Either a design oversight by SONY, or they just didn't expect these receivers to be around 50 years later.)
It is true that the ends of the glass are painted green. Green glass paint from a craft or art store will restore it to the original look. I've tried green LEDs and don't like the look. It's the wrong green and the light cast on the dial is patchy and shadowy, due to the more direct light projection of LEDs vs incandescent and lack of anything to diffuse the light. Use the paint if you want the original look.
Once painted, a soft white LED (festoon lamp) will give the right look and won't give off enough heat to peel the paint / burn the reflectors. You can cut new reflectors from reflective, non-conductive card stock, also available at craft and art stores.
Here's how repainted glass, soft white LEDs and new reflectors (cut from reflective card stock) look on the dial of an STR-7055:
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