What do you think, is this true? Will the 16 GB be comparable to my current 32 GB?
If your current work actually benefits from 32GB of RAM on an Intel Mac then you will probably benefit from 32GB RAM on an Apple Silicon Mac. The RAM needed by applications hasn't changed much and if that adds up to more than the amount of RAM in your machine, it will start swapping chunks of RAM in and out of SSD storage, which will
always slow things down.
However - you're upgrading from an obsolete 10-year-old Mac, and a new Apple Silicon mac, even a 2020 Mini, has faster processor cores, faster GPU cores, new hardware acceleration for some functions, faster SSD and RAM access etc. (which does reduce the impact or running out of physical RAM) and so may
still turn out to be faster at your work than a 2012 Mac Pro, might let you have more apps running, open more browser tabs etc. even with only 16GB RAM - but
if you are actually using more than 16GB of RAM, then you still won't be using the CPU/GPU to it's full potential.
Apple Silicon is certainly a bit more efficient at dealing with low-RAM situations than intel, but the ridiculous "8GB on M1 = 16GB on Intel" myth came from people comparing the speed of jobs that weren't using more than 8GB to start with - often video encoding jobs that were massively accelerated by hardware codecs in the MA - also, at the time, there weren't any M1 Pro/Max chips with 32GB to compare with. People also get misled by the memory stats from Activity Monitor - its really only the "Memory Pressure" that counts.
It looks like a 16GB Mini would be more than enough for your current use, and is still quite capable of doing serious stuff in Logic. However, you're talking about "downsizing" from a mac that cost $7000 new to a Mac that costs $1100 new - i.e. you're going from a top-of-the-range Mac to a mid/low-end one. You might very well get away with that - but I'd at least investigate the Mac Studio as a more obvious upgrade from a Mac Pro (still $2000 vs $7000). It's not just RAM, you get more processor cores, more ports and support for more displays.
Also, there's a lot of speculation about M2 Mac Minis (which would probably go up to 24GB RAM) and M2 Pro Mac Minis (which would be more affordable than a Mac Studio) coming soon - unfortunately nobody knows for sure if or when they will turn up (personally, I don't think Apple will launch a M2 Pro Mini while the M1 Max Studio is still relatively new).
What does it change that RAM is shared with the GPU? Is theoratically less of it needed because of this?
Theoretically, you need
more RAM c.f. something like a Mac Pro that had dedicated GPUs, since older machines came with several gigabytes of dedicated video RAM and some of those requirements (framebuffers etc.) still have to be stored somewhere. It's possible that up-to-date software will be more RAM-efficient by (e.g.) not having duplicate copies of stuff in main RAM and VRAM but you'll still lose some main RAM to things previously held in VRAM.