PieFed has some features that I find helpful in this regard.
One is the Categories of Communities. You'll only see News in the News category or in the non-category search methods (standard Subscribed/All/New/etc.).
Another is the ability to follow - and arguably more important unfollow - everything. Including communities, posts, people, etc. I once made the mistake of replying to a comment in ChapoTrapHouse@hexbear.net, and another in Lemmygrad.ml, and the replies kept coming for WEEKS and WEEKS - I almost quit the Fediverse entirely at that point, and I hear that scenario repeated by others as well. But on PieFed, not only can I unfollow any conversation at any time, but unlike Lemmy it also allows a true blocking of all users from any instance you choose (edit: to clarify, I mean without requiring an admin to do it for you and everyone else on the same instance at the same time - a personal defederation that affects nobody else, just like a block, except that Lemmy doesn't allow blocking users from instances, only communities from instances which is nowhere close to being the same thing).
Ofc nothing is perfect - e.g. I decided to unfollow poetry@lemmy.world bc I don't want to read 5 of those in a row every morning, and rather would want to savor just one at a time. Also it would be nice to separate comment replies (that seem more urgent, for the sake of an active conversation) from e.g. a new post that you haven't seen yet? But for a true niche community, with let's say less than a handful of posts every day and you want to be notified about every single one? It seems perfect for that.
The UI for PieFed needs far more polish, especially outside of the narrow range of short comments on posts with few of those in number. e.g. far too often the existing notifications don't work as the reply to your comment got buried away onto some other page entirely, in an effort to streamline reading but then that not interacting well with the newer (unfinished?) notifications feature. But while it lacks much polish that Lemmy's UI and apps have, it also has so many features like those mentioned above that Lemmy lacks as well, and may move faster in its development due to using a more common programming language. It is so nice to have choices to pick from:-).
Otherwise on Lemmy you could make alts, like one subscribed to News communities, another for Memes and Shitposts, etc. Blocking users would get super annoying bc you'd have to do it multiple times. Blocking the largest news communities and the accounts that usually fill them, and then sorting by New can help, but it requires enormous curation efforts to get there and even then falls far short of what you asked - e.g. you also, still have to bookmark or otherwise check each one of your highly active communities one by one (edit: I mean niche ones here, bc the chances of seeing a post there on New can still be slim, if you are concerned about seeing EVERY post there rather than just find something to read from across hundreds of subscribed communities, so different solutions for different workflows).
Lemmy is great for checking memes, reading tech or politics news, and liking Linux - but for everything else it needs improvements to be made to support. I'm not going back to Reddit though:-).