Why is Google still showing my old website?

There are a lot of things to go into ranking a page. A lot of it takes time for the algo to work out. In the past, Google was typically very eager to make assumptions about most sites when it discovered new content Basically, it would say, "Okay, the on-page stuff says this and this... I'm not sure what the off-page and stuff we need to verify is going to do, but we'll make assumptions that it's going to do this, this, and this based upon other things we know about this site." And then the page would rank within days or even hours. It may not rank exactly where it was finally going to end up after the stuff that takes time gets sorted out - but it would rank nonetheless. In the past month or two, Google seems less eager to "trust" and make assumptions about new content without qualifying signals and other things going on. These things can be stuff like structured data that validates and confirms what the NLP functions have discerned from the copy, site information architecture and topic clustering (i.e. is this page in a spot on the site where I know other pages are talking about something similar to what we think this page is probably about?), establishment and breadth of your brand entity (i.e. Does what we think this post is talking about fit within what we know with absolutely certainty that is something this brand covers?) and various other things that go far beyond the "Research Keywords, Put Keywords into a post, Publish Post, Rank!" type strategy. From what I'm seeing - these sites that are having trouble are not ones that send consistent confidence signals. The posts will likely get indexed and ranked eventually, but you have to wait for Google to do the "long game math" before it'll do so. And, rather than totally tanking your page while it's waiting to do that - it's at least leaving the old one and what it knows about that page in there and letting that rank for you. It seems similar and on-target enough that, while it's not confident enough to make all the assumptions it needs to rank the new stuff, that it's likely to be similar or better than before - so we'll make that assumption and keep it ranking based upon the old data. Now... this whole thing is pretty new so I can't say with absolute certainty that this is "exactly" what's going on right now, but it seems more and more likely that something similar is happening - something that is at least in the category of "Confidence" or "Confidence Adjacent".