700w psu , hmm if it was not for the fact that you have used the system a long time ,
added to the fact that you do say its crashng when not on full load ,
i would be tempted to say the psu is not man enough for the job , the psu in the system i am using is max rated at 1300w its also fair to say that with the gpu and cpu’s running at 100% the power consuption is arround 1,000w
beeing a hardware engineer by trade , myself i would strip down the psu and see if its got any bloated /leaky caps , that do degrade the psu’s over time, and 11years old as you say so arround the time the bad ones where still in cerculation (theres a story to that but too long to post here), but its far to say if your not skilled then its not something i can recommend doing , high voltages and such that stay charged when unpluged for weeks sometimes ,
the easyest way to solve issues like your having is not something you can do ,
but you would need a known working system to the same spec, and swap in the suspected part till the error starts to show on that ,
but only ideal when you have a few the same systems kicking arround
otherwise from a repair point of view
again replace parts till you find the faulty part , then replace the old parts other than the replacment faulty part and retest ,
that way the customer only gets charged in the end for the actual faulty part , rather than all the bits needed to find that out ,
beeing without the bits to try then its going to be hit and miss ,
so is it the gpu , or the psu when using that gpu or is it still another problem , maybe you do need to look at sending it to a service center or repair shop that would have the parts on hand to do this (covid hassles and such but you could arrange shipping to them if complealty stuck)
changing the gpu to a lower spec one may show it works with that
but thats not takeing into account the psu load , the only way to find that is to fit another gpu of the same spec and see then if the issue persists , borrow one to try if you must , there not cheap atm
quite often from experiance it often tends to turn out to be something you did not initaly expect ,
on that note i would be tempted to invistigate the power /reset button issue again , ensure no cable or connector issues , bad connections are intermittent and somewhat random , and top of the list of issues that are a real pita to find and solve , also ram , you sure the ram is not getting too hot and the crash beeing the result of memory errors , changing the gpu etc may inadvertanlty give the ram better airflow so it does not crash as frequent , i would love to be able to pinpoint the issue directly , but such is the case that it could be any one of a wide number of posibilaties that cause the issue , and only realy found when you hit upon changing the actual faulty bit and the problem goes
given also you say your system is 11 years old , (mostly but not all parts ) rather than buying all the suspected parts (mobo, cpu ,gpu , psu, case ,ram) (11 year old parts are not new so may be faulty anyway) you may be better looking on ebay for a base system unit with the base spec (ram and disks aside ) ex lease refurbished workstation (3 to 5 years old)(should come with a garanttee) ,that you can use the bits on hand to upgrade it to the same spec (existing gpu included) , plus getting a new machine ( to you ) in the progress , i know it will cost (£700 to £1200), but your stuck with eather the cost of getting bits to test an old system , and the time , the gpu’s are the issue atm dew to the global chip shortage , even if it turns out to be the gpu in the end , a replacment gpu atm can cost well over the price of such a base system alone atm , even secondhand can be well over £1500
personly i try to replace my system every 5 years even if its a 5 year old machine to start with, not only for new spec things like faster sata/sas , faster pci/e and other such new features , replacment part availabilaty (usualy still new parts are still available), but also because of driver support , often older systems get dropped from current driver support , not shure if thats part of the issue your having atm
anyway i feel we digress from topic even more , as much as am willing to help , maybe you would be better looking for answers on freenode irc chat chan ##hardware the guys there could give you pointers regarding your hardware issues , and it is a more suitable place to discuss them than here