You can always try a reflow to save it long term but be aware there is a very real risk of doing further damage to the motherboard, but if you’re okay with it failing again and again and just want to run it longer, it can help extend the life of a dying motherboard at most. What this does is reflows the solder joints on the board, it doesn’t fix the core issue the GPU flip chip balls failed. You’re usually better off pulling the hard drive when the GPU fails and letting it go for parts.
If you care about the computer or it's critical then don't try this. It's temporary to start, and it risks further damage. Since it's dead, you might as well try and see what goes on with it.
While most techs don't recommend this (myself included!) I don't mind mentioning it as a last resort fix for things like recovering files from a Bitlocker drive or just to bide a little more time but the laptop or GPU needs to be replaced ASAP! That said a lot of “refurbished” boards tend to have the same issue but were baked so you’re just not paying someone up the nose to sell you a baked board which won’t last if you do bake it at least. THIS IS NOT A PROPER FIX, PROFESSIONALS. These boards will keep dying once baked!!!
Here is your service manual for the computer. While that's not for the 14z, they're basically the same.
Look at the manual to gut the laptop. Remove EVERYTHING from the computer. Yes, this includes the stickers and labels off the board.
After doing this, preheat your oven at 400 degrees for 5 minutes. While you do that, put your motherboard on a cookie sheet you don't mind never using for food again with something to keep it up — anything stable is fine. The board needs to go chip side up since that's the side you want to reflow.
Put some liquid flux under the GPU(if there) and southbride. Only use enough so it flows under the chip. This will help the reflow life out quite a bit but you need a “no clean” flux or an ultrasonic cleaner (both preferred).
When the oven is warm, put the board in for 5 minutes. Set a timer and don't let it sit.
When the board is done, remove it carefully and let it cool for 2-3 hours or longer. You can tell if it's cool by the solder being solid and not molten. If you bump the board while the solder is molen it’s trash. When it's cool use good thermal paste on the CPU and copper shim the GPU to keep the temps down further. After you do this, plug the fan in and reverse disassembly. Run it until it dies and look for a new laptop in the meantime — again this will not last.