There is so much wrong with this that I don't even know where to begin.
I don't intent to be rude, but this is just not how you build a decentralized/distributed system. The network would grind to a halt if every user app had to search recursively through a portion of the network, and aggregate & rank posts by itself. Aggregate values (communities, votes and so on) would never be right, because you'd never be able to acually gather all events for a particular entity in time. This might work in a local network of 10 nodes, but not on a global scale.
On top, who would pay for those nodes you are querying? There is no relationship between the users and the nodes, so why would anyone just run a node for others or be willing to pay anyone else in this scenario? Servers cost money and stuff. And your spam filtering and moderation solution would be the exact same as with instances, so nothing is gained here.
Maybe have a look at the Session messenger and their Oxen network. They go to great length to make sure the work is equally distributed among nodes and they are compensated fairly. This doesn't just happen magically by itself, and there are many bad actors who will try to exploit any weakness they can find.
So I just think it's impossible to create something like lemmy in an anonymous way, because content moderation is a human decision. There is no one correct mathematical solution, and I also can't send some kind of filter query to a server to do it for me. All I can do is read the general rules that another human being has wrote up, subscribe to their moderation "service", see how they are doing, and decide to stay or switch to another.
Similarly, if I don't want to aggregate all the posts in the world by myself (as you are suggesting), then I'll have to fine someone to do it for me, and somehow pay that someone for their service. This part is actually kind of solvable (again look at Session), but it is not straight forward at all! It would involve crypto currencies, mining/staking, and some kind of client-side monetization. For this part I think trusted instances are just a much better solution, because we are building a social structure here anyway.
If you decide to go down the Synology route, make sure it supports docker. Their cheaper models don't support it, and it's the gateway to self-hosting all the services that are not available directly from the package manager.