Upgrading from a RTX 2060 to a 6750 XT. Do I need to immediately upgrade my 600w power supply as well?

For context, I’ve had a Corsair CX600 for about 8 years now. I also currently have a AMD 3600 CPU. I started with a GTX 970, then RTX 2060, and now I am planning on buying a 6750 XT. Do I need to immediately upgrade my PSU as well? I have had no issues up to this point, but worried that, with the amount of time I’ve used this power supply, and with a more powerful card, I will have to upgrade immediately, or it could damage my the rest of my computer.