Lemmy doesn't have a concept of what a "post like this" is. It only categorizes posts based on simple statistics like "number of recent votes", which I believe drive the "hot" ranking or number of recent comments (active), or the date of the post.
Creating a concept of a "post like this" would generally require an AI/ML classification pipeline. This kind of thing is common at big social media companies, but it's pretty computationally expensive compared to regular browsing. It's also somewhat ideologically fraught as it's the same tech big social media companies use to create algorithmic echo chambers and drive unhealthy engagement. I realize your proposed use-case is pretty innocuous... but I suspect many folks will extrapolate to view the proposal through that lens.
I don't see folks champing at the bit to immediately add a feature that would add to the capacity woes the biggest instances are already feeling, but I'm equally sure you're not alone in desiring features that would need to be built on top of classification pipelines. Maybe someday Lemmy will have one, but it doesn't exist today.
Edit: Maybe a less general approach to this would be to offer a weighting for each community, and lemmy would skip some percentage of posts to that sub in your feed. This isn't how most commercial sites would do this, but it's simple and maybe close to what you want. It also doesn't exist today though.