This may not be safe.
A bench power supply has current limiting. With this unit you're not protecting yourself and the circuits from excessive current.
You can buy adapters specifically for this purpose. Some of them are fused and have an on-off switch. I've used them - they work perfectly. I'll see if I can find a link.
OK, it seems to be a good idea to fuse each rail of the PSU. Chat GPT suggested 25A car fuse for the 12V rail, 20A car fuse for the 5V rail and 30A car fuse for the 3.3V rail. Will this be okay or do you guys recommend something different?
Don't do it. There are good budget options from Korad to have a decent (linear) bench PSU. If you need lots of power, then the adjustable switching PSUs from Gophert or Rek are a good choice. You might want to replace the binding posts on any of my suggestions though. 
I am mostly doing this for learning and to feel good since I always wanted to convert a PC PSU. Realisticly I probably don't need a bench PSU. My use cases are somewhat limited as I mention further bellow. Also thank you for the recommendations I will keep them in mind for the future

A bench power supply has current limiting. With this unit you're not protecting yourself and the circuits from excessive current.
Hm. I've converted about a dozen AT PC-PSU's to variable voltage (2.5-28Vdc), variable current (0-10A) power supplies. Wasn't that hard. All supplies were based on the TL494 (=KA7900). The trick to add (adjustable) current-limiting to the circuit was to add a short bit of sensing wire in the transformer's ground return, and use one of the unusued comparators in the TL494. Worked a treat. If you want to know more about this method, search 'Oztules PC PSU conversion', you'll probably end up on the old forum fieldlines.com
But reading the original question of OP, I suspect this kind of modification is a bit beyond his skill-level at the moment.
I've used those modificied PC PSU's for many projects: lab power supplies, capacitor-discharge spotwelder (to recharge the 1.56F capacitor bank), in a CNC-controller, etc. Some were converted to a 15-50V dc and 50-350Vdc supplies.
I must admit that, on occasion, some conversions weren't entirely succesful, with bits of exploding semiconductor flying all over the place.... Anyway, it is possible to modify these PSU's to adjustable voltage and adjustable current-limiting. Would I do it again these days? Probably not....
Did ChatGPT also tell you that an ATX PSU's ground is connected to earth/PE? And why that could be possibly a bad idea for a bench PSU?
You guys gave me a headache xD. I think messing with the PSU circuitry is way above my skill level and probably overkill for this project hence the use of cheap back-boost converter. Also isolating the GND is too expensive or hard for me and probably overkill as well for this project. IK chat gpt is bad which is why I posted here but it's convenient AF for noobs.
I plan to use this PSU only on household devices (cheap battery devices) like toys, cheap DC RC motors, laser pointers, cheap flash lights etc.
Thanks to you guys I've added some rules for using it:
1. don't use it with more than 1 device at a time
2. don't use it with expensive devices
3. use the USB TYPE C to charge only smartphones and tablets
4. be careful not to ground a device connected to the PSU. I should place it on non-conductive surfaces and touch it only if I am 100% not grounded.
I also plan to power breadboards with simple circuits and maybe more complex ones in the future, is this use case ok or should I use batteries instead?
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I understand that it will have a high risk of frying a device, that it is not meant for a PC PSU, but is there also a high risk of frying the PSU itself even with the added car fuses? Is there anything else I can easily or cheaply do for added safety or even rules to follow?
As I understand my plan should work but with a big asterisk on safety, correct?
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Thank very much for your knowledge guys and enlightening my noob *ss
PS Sorry if I misunderstood anything as my elctronics knowledge and understanding is very poor