I personally found that a lot of these power supply recommendations are based on builds with a power hungry Intel i9 processor such as the 3080, for example. I only plan on pairing a 6800XT with a 5600x, standard air cooling, standard clocks, and nVME SSDs so its actually a pretty modest build in terms of power consumption. I just wanted to see if there was some verification from others more knowledgeable on this subject.
There is a disclaimer on Nvidia's website that says the card may obviously work with a lower configuration. The 6800XT does use 20 watts less than the 3080, which wants 320w max.
According to Guru3D at AMD Ryzen 7 3800X review - Power Consumption and temperatures, they state that even the 3700x only drew 165 watts under a multi-threaded load which means it should be safe to assume overall that a 6800XT combined with a 5600x, plus the ram and hard drives, realistically will only come out to a max of 500 watts.
Power recommendations have to be high because there are -a lot- of garbage PSUs out there which have a rating that's nowhere near justified, such as being obtained by combining the 12v, 3v, and 5v rails despite 3.3v and 5v supplying very little in a modern system.
If you figure the 6800XT at 375w, 5600X at 125w, and motherboard and other resources at 100w, you're fine with your 700w PSU IF the +12v rail is rated for 50A or more.