The path to the developer directory is /Applications/Xcode.app/Contents/Developer, not ...Developers. (no 's' on the end). You do need to point at an existing directory. If you are using Xcode 14, and you renamed it Xcode14, your command should be
xcode-select --select /Applications/Xcode14.app/Contents/Developer
When you install command line tools, they are installed into the currently-selected Xcode. You are saying "my command line tools in Xcode are Xcode 15.3". Which Xcode do you want to use? You said you switched from Xcode 13 to Xcode 15, but you're using Xcode 14 - which is it?
You can use multiple Xcode versions on one machine, but you have to be careful about running multiple xcodebuild commands at the same time if you want to target different tools, because the xcode-select command is system-wide. If you launch Xcode from Finder, you'll use the one you launch, you don't need to set anything. If you run xcodebuild at the command line, it will use the selected Xcode, which by default is the one in /Applications/Xcode. I usually make sure that the Xcode I use on a daily basis is actually called "Xcode", and any beta or previous versions I have lying around have a different name.
It sounds like your build script is specifically looking for an app called "Xcode14". Maybe whoever wrote it named their Xcode "Xcode14". That's fine, but then you have to do the same thing (which is pretty strange if you're actually using Xcode 15), or change the build script. I know what I'd do...