I would suspect the PSU first. When troubleshooting possible hardware issues, you always start at the wall. Is it plugged in? Is it turned on? Are you delivering good, clean stable power to the electronics? Obviously, it is plugged in and turned on. But the only way to determine if your PSU is delivering good, clean, stable power is to swap in a known good PSU and see if the problems persist, or go away. Since EVERYTHING inside the case depends on good power, you must start here.
how old is the thermal paste?
Doesn't matter. It is a myth (and often a risky one too) that TIM (thermal interface materials) needs to be replaced because it is X number of years old. Folks really should just leave TIM alone.
AS LONG AS the cured bond between the processor and the heatsink is not broken, there is no reason to replace it. Even if it is 10 years old and dried out, the solids left behind are still occupying the microscopic pits and valleys in the mating surfaces, preventing insulating air from getting in. In other words, the TIM is still doing its job. If you truly "need" the few degrees a fresh application of new TIM "
might" provide to prevent crossing over thermal protection thresholds, you have other, more urgent heat issues to deal with first, like case cooling.
I note there is not a single TIM maker, motherboard maker, CPU or GPU maker, or cooler maker that recommends or even suggests replacing the TIM after X number of years.
The problem is, it is too easy to have a mishap that damages the processor, causes excess TIM to get on where it should not be, causes the heatsink to be improperly remounted, etc. All for something not needed. Best to leave it alone so that cured bond does not get broken.
That's fine, Contrary to what many want us to believe, OEM/stock coolers of today are more than capable of providing adequate cooling for the processors they came with AS LONG AS the case is providing a sufficient supply of cool air flowing through the case. So make sure the case is clean of heat trapping dust and your fans are spinning properly.
I note HWiNFO does show some extremely hot temps, but they are so high (127°C), most likely they are false readings. You might see what another monitor, like Speccy, says.