To start, I would say "no way" to the RTX 3050 unless that's the one that your friend will sell you for cheap because those are so overpriced that they're not even worth looking at.
The truth is that no matter what you get, that R5-1600X is going to bottleneck the hell out of it. An R5-1600X with an RTX 3090 Ti would get worse gaming performance than an i9-10900K with an RX 6600 and that is NOT an exaggeration. Here's a video from Tech Deals demonstrating how an R7-1700X bottlenecks an RTX 3090 Ti so badly that it loses to an RX 6600 which itself is also bottlenecked by an i9-10900K:
Now, you're not being very clear about which card your friend is offering you and I don't really know why you would withhold that information so I'm going to ignore it.
The RTX 3050 and RTX 3060 are both bad values. They both cost more than Radeon cards that out-perform them and neither of them should have the "RTX" prefix because with RT turned on, they're so weak that the 3060 is almost useless and the 3050 literally
is useless.
Now, I don't know what country that you're in so I'm going to just use Germany because you gave your budget in Euros and Germany is right in the middle of Europe. If you are from there, please forgive the fact that I didn't call it Deutschland.
I'll demonstrate to you just how bad the values of the RTX 3050 and 3060 are:
The RTX 3050 costs
277 € <-Click the price to see the PCPartPicker listing
The RX 6600 costs
274 € <-Click the price to see the PCPartPicker listing
Ok, so both cards are similar in price with the RX 6600 being 3 € less expensive. However, they're not even remotely close in performance because the RX 6600 is, on average, a whopping 29% faster than the RTX 3050 8GB according to the
TechPowerUp GPU Database. This makes the RTX 3050 a terrible choice.
With the RTX 3060, things get better than the RTX 3050 but still not good:
The RTX 3060 costs
349 € <-Click the price to see the PCPartPicker listing
The RX 6650 XT costs
321 € <-Click the price to see the PCPartPicker listing
So the RTX 3060 costs 28 € more than the RX 6650 XT but, according to the
TechPowerUp GPU Database, the RX 6650 XT is 14% faster. The RTX 3060 has 4GB more VRAM than the RX 6650 XT but that's not going to have any impact on 1080p gaming (which is all you can do with a GTX 1060).
Compared to the GTX 1060, again from the TechPowerUp GPU Database:
The RTX 3050 is 52% faster.
The RX 6600 IS 77% faster.
The RTX 3060 is 109% faster.
The RX 6650 XT is 239% faster.
Regardless of what you get though, that R5-1600X would mean that you wouldn't see a performance increase in gaming that would be even close to what those other cards are capable of.
Now, what I was thinking was that your best bet would be to get an RX 6600 and a Ryzen 5 5600. The R5-5600 costs
142 € and together with the RX 6600 only costing
274 €, you'd be looking at 416 € which is well within your budget range and would be the best upgrade that you could get for less than 500 € and better than ANY video card by itself. The best part is that all you'd have to do is some BIOS updates and drop the R5-5600 into your existing AM4 motherboard. You don't have to buy a new motherboard or new RAM. This is the wonder of the AM4 platform!
Now, you could get the RX 6650 XT for an extra 47 € and still be under 500 € (463 €) but I really think that the RX 6600 would be best for you. There have been questions about your PSU but the RX 6600 would work fine with the PSU that you have. I know this because your GTX 1060 works. The GTX 1060 and RX 6600 both recommend a 300W power supply which means they they draw about the same amount of electricity. Your power supply would be guaranteed to work with the RX 6600 so it's one less thing to worry about.
My recommendation within your 500 € budget would be a Ryzen 5 5600 CPU and a Radeon RX 6600 GPU. At 416 € for both, you can't go wrong.
TechPowerUp GPU Database Listings:
GeForce GTX 1060 3GB
Radeon RX 6600 8GB
GeForce RX 3050 8GB
Radeon RX 6650 XT 8GB
GeForce RTX 3060 12GB