I found a mini PC on amazon ( ACE Magician ARM5 Mini Gaming PC ) that i can replace my curent potato PC . It has integrated Vega graphics , and i'd like to know if it's good enough for non 4K gaming .

Depends on the games you play. The quickest way to look up exactly what APU it has and type that into Youtube with the word "benchmark" or "gaming", etc. Eg for 5600U:-

https://www.youtube.com/watch?v=hSKcULW9PPk
https://www.youtube.com/watch?v=_BVvbSIaL7A

As with all APU's there's a lot that will run on that, but also some people are over-optimistic when it comes to new AAA's / resolutions. You said "under 4k", yet there's a world of difference in playability between 720p vs 1080p vs 1440p for APU's. "U" chips are like 15-25w mobile chips, so you have to keep expectations real there regarding turning the settings down / upscaling.

What, this one?
https://www.notebookcheck.net/Ace-Magician-AMR5-in-review-Stylish-Mini-PC-with-a-Ryzen-5-5600U-and-discreet-RGB-lighting.648972.0.html

Absolutely for most games on 1080p.

I have a Ryzen 3 2200U and even it is capable of gaming, though less demanding ones of course. I've run APU's for over 10 years now and they are more than enough for gaming, believe me.

The other one . As for a plus storage : a 1TB Crucial Internal Solid State Drive My monitor only supports the 1920x1080 resolution .

You should be OK. You'll find many older games will run natively at 1080p/60 whilst some new heavy games may need turning down to 720-900p. Best thing you can do is to type the name of the game into Youtube along with the APU for the ones you're most interested in. Eg:-
- Dishonored 5500U
- Bioshock Infinite 5500U
- Prey 5600U

^ It will give you some idea of what 'weight' / era of game runs at what fps. As you can see, 2007-2012 era FPS's have no problem staying above 60fps but Prey (2017) is below and needs tweaking / upscaling if you want a locked in 60fps.

It isn't far between 4500U and 5600U so still yes, both 720p AND 1080p. Visually speaking you won't notice much between those two resolutions depending on the size of your monitor/screen, so going lower on the resolution you can often keep a higher graphical profile vs going 1080p and have to go low-very low, but that depends on the game.

https://www.youtube.com/watch?v=Ci7J-psiAW8

EDIT: If you can get the one with 5600u I would recommend at least that one, but again, depends on what you want to invest in it. On miniPC's you often pay more for small factor and get less performance. Depending on what you already have, it might be cheaper to just get an upgrade pack of CPU+RAM+Mamaboard.

What's the price of it?

The one

with Ryzen 5 4500U costs €424.15 minus €50 with discount coupon
with Ryzen 5 5600U costs €659.99 no extra discount coupon code

there's also a mini pc with Ryzen 9 4900H on amazon for €769.00 minus a €115 discout coupon code

There are many older games that will run on a APU just fine. Also, this specific APU seems good to go for ps2/gamecube/dreamcast emulation, in case that tickles your fancy.

IGPUs have come a long way. AMD still seems to be spanking Intel's low efforts. This video shows how well something like the Ryzen 7 5700G fares in games. As expected, it ain't king but it does fairly well, and should also be perfect for less demanding indie games or older games. In comparison the Ryzen 5 5600U, should be still fairly competent but not quite as fast.

What I'm really curious to see is how AMD's APU will fare once they'll really switch from Vega to RDNA. I know the Steam Deck is kind of an indicator already how well a full-on desktop chip might do. That said, hopefully AMD will stop the OEM-only shenanigans for them as only their late CPUs with Vega 8 were directly available to consumers.

The 4500U one for 374 is actually not bad considering it's a full computer with 512GB NVMe and 16GB(!).

Seems I found the 5600u one for 422 (euro and dollar is the same):
https://www.amazon.com/Gaming-Ryzen-5600U-Windows-Computer/dp/B0B6NRNGPL/ref=sr_1_1?crid=HOWQB2HCQ186&keywords=Ace+Magician+AMR5&qid=1667676462&sprefix=ace+magician+amr5%2Caps%2C450&sr=8-1

Damn, why must it be so darn expensive to get one of those across the border these days. Now I have to pay 131(eurodollars?) just to get one shipped to Norway. Love that case on these Ace Magician AMR5. :D

But if the most bang for the buck is important then perhaps this is something to consider...? A combo with CPU+RAM+Mamaboard for about 260.
https://www.amazon.com/AMD-Ryzen-5600G-12-Thread-Processor/dp/B092L9GF5N/ref=sr_1_1?crid=1PU9FLV2KNA63&keywords=ryzen+5+5600g&qid=1667675908&sprefix=ryzen+5%2Caps%2C269&sr=8-1

The Ryzen 5 5600G have sunk really much in the last few days/weeks and is at -50% now. Assuming you can use the case and the PSU, and you don't mind building yourself.

But to recap - yes, the integrated Vega is good for budget gaming.

That would be incompatible with the potato's motherboard .

Hmm . How about this mini pc ? Or the Ryzen 7 3750H isn't a good choice for gaming ? I don't play online games , don't want to play the newest GTAs , Forza or Cyberpunk .

An upgrade is complete with CPU+RAM+Mamaboard. Look just under the picture of the 5600G, "Buy it with":
AMD Ryzen 5 5600G + Corsair Vengeance LPX 16GB + ASUS Prime B450M-A II for 263.

Sure, like I wrote, here you pay for the size, not performance on these minPc's, and Ryzen 7 > Ryzen 5 > Ryzen 3

What I am trying to say is that you don't normally buy these miniPC's for gaming only unless you want to compromise performance for size and cost, (or have a wife that doesn't like big computer cases beside the TV in the living room :D).

4500U is good but not very future proof (even for small RPG's and demanding card games) that's why I recommended the 5600U if you can get it at a better price than 600+.

Haha .

Noob question : Is it possible to connect a mini PC with an external HDD ( for example Seagate FireCuda ) to have more storage space ?

If it has a standard USB port, then it should be.