Am I safe to plug a different PSU in
You, yourself, are safe, provided you remain at arm's length when switching on the computer with a new power supply, just in case something else goes bang and emits magic smoke. Or did you mean "is the computer safe?" That's a different matter entirely.
I had an old PSU go bang in a second hand computer recently. It took out a 13A fuse in the mains plug. I connected a new PSU and the Xeon server board and GPU booted back into Windows normally. I was lucky.
is there a chance the components caused an issue?
PSU components failing spectacularly, yes. Components outside the PSU on the motherboard or GPU causing an issue, probably not. There are all kinds of protection circuits built into ATX power supplies, e.g. over current, over/under voltage, over temperature, etc.
When a GPU card or motherboard fail and go short circuit, the OCP (Over Current Protection) in the PSU should operate. The power supply should shut down and no smoke should be emitted from inside the PSU.
It's a completely different matter when the PSU itself fails, generally due to old age. Protection features may not work if an electrolytic capacitor explodes or PSU components such as MOSFETs, varistors, MOVs, resistors, transformers, inductors, relays, etc., go up in flames.
There's no easy way of telling if your computer has survived until you change the PSU. As
@Lutfij says, carefully inspect your mobo, GPU and disk drives for burnt components before proceeding, but I doubt you'll see any visible signs of damage. Do not use any modular cables from the old PSU.
Take care.