There's a credible IEP report (assuming this is what you're referring to) which asserts 1 billion displaced by 2050. This is probably the report cited if you've seen this assertion in articles.

It should be clarified that's worldwide over the course of several decades. Up 3.7% over last year excluding Ukrainian refugees. I think the slower migration will help to offset some of these social pressures you're projecting.

This article does a pretty good job at illustrating which regions will be affected by this migration

TLDR again: Not so much gloom and doom. Some places are going to grow. Africa will see a boom.

Reddit tends to conflate climate change with climate disaster. I'm not saying climate change shouldn't be taken seriously, I'm just attempting to take some of the hysterics out of this situation, because if you believe reddit we're all doomed and we shouldn't even try... which just isn't true.