There is no way to "ugrade" a 2011 Mini to a 2020, you would have to buy a new computer. If you buy new direct from Apple, the cheapest 2020 Mini is $799. Apple has a trade-in program that you can check, but you will get virtually nothing for a 2011 Mini.
Mac mini with the M4 and M4 Pro chips. Built for Apple Intelligence. With front and back ports. Get credit when you trade in an eligible Mac. Buy now.
www.apple.com
As usual, you need to shop around. Big retailers often have discounts on the Mini. Here in the US, B&H Photo currently has this same model for $759, for example.
Apple also sells refurbished Mini's that have the same warranty as new. I have seen these as low as $600, but they have the smaller 128gb internal SSD that has been discontinued. They sell very quickly, so you need to constantly check Apple's site and be prepared to buy immediately when you find one. They have a lot of different configurations, and it might take a month to find the refurb you want. Most of the time, there are none listed at all.
There is not much you can do on a mac mini from 2011 to bring it up to date. This would likely be a big project that would go with replacing the motherboard, likely having to build one yourself from the ground up (which is near impossible. And is impossible if you don't have a related engineering masters degree, most likely). Moral of the story: it is not worth it.
If you are alright with buying a new one, you could sell you online for twice or four times more than what Apple would pay for it. @Boyd01 made some compelling arguments there. but I would recommend, if you are after the performance your 2011 can't deliver, to get a 2018 model, the most recent one (4th generation, you can differentiate it because it's the only one with USB-C). It will still not be a powerhouse, but is it the most recent one and will likely be supported by much longer than the other options.