Multiple rust-analyzer installations

I am slowly moving from VS Code to Zed. That rather quickly brought up some issues with the rust-analyzer that led me to discover that I have about 4 different versions of rust-analyzer on my machine. Or, perhaps I should say I had (past tense) 4 different versions. Now, I have the binary in my favorite ~/bin dir. And here's where it gets weird. I just cranked up VS Code and it wants to install a new rust-analyzer binary. Here are my settings.json entries that should/might be pertinent:
// Rust
"rust-analyzer.server.path": "~/bin/rust-analyzer",
"rust-analyzer.assist.emitMustUse": true,
"rust-analyzer.cargo.features": ["all"],
"rust-analyzer.cargo.buildScripts.overrideCommand": null,
"rust-analyzer.completion.fullFunctionSignatures.enable": true,
"rust-analyzer.diagnostics.enable": true,
"rust-analyzer.inlayHints.closingBraceHints.minLines": 1,
"rust-analyzer.inlayHints.bindingModeHints.enable": true,
"rust-analyzer.inlayHints.closureCaptureHints.enable": true,
"rust-analyzer.lens.references.adt.enable": true,
"rust-analyzer.lens.references.enumVariant.enable": true,
"rust-analyzer.lens.references.method.enable": true,
"rust-analyzer.lens.references.trait.enable": true,

Here are the warning/error messages that the VSC plugin is screaming about:

Unable to read file '/home/rl/.vscode-insiders/extensions/rust-lang.rust-analyzer-0.4.2310-linux-x64/package.json' (Error: Unable to resolve nonexistent file '/home/rl/.vscode-insiders/extensions/rust-lang.rust-analyzer-0.4.2310-linux-x64/package.json') (yes, I know you can't find it there. I deleted it on purpose. Why aren't you looking in ~/bin like I told you in settings?)

And the other warning: The update for rust-analyzer extension introduces executable code, which is not present in the currently installed version. Please review the extension and update it manually. (What? Please, will everyone stop trying to install binaries all over my machine without me either compiling it myself or curling it from a known repo?).

So look. All I want is ONE install of rust-analyzer. It is in my ~/bin directory, and I now want to map VS Code, VS Code Insiders and Zed to that one binary. What am I missing?

I should add that right after typing this, I cranked up Zed for the first time since all this cleaning up, and it had no issue finding and implementing the rust-analyzer binary sitting happily in my ~/bin directory.

That is the rust-analyzer vscode extension you deleted, not the rust-analyzer executable. Vscode always installs extensions to ~/.vscode-insiders/extensions and doesn't look anywhere else. rust-analyzer.server.path is used by this extension. Without the extension installed in ~/.vscode-insiders/extensions nothing will read rust-analyzer.server.path.

The extension ships with a copy of rust-analyzer by default. (as in the .vsix extension zip file itself contains the executable. vscode unpacks it into ~/.vscode-insiders/extensions and when you uninstall the extension it is gone again) If you set rust-analyzer.server.path it will not actually be used and you can safely remove the binary itself (but not the rest of the extension) without affecting any functionality if you have rust-analyzer.server.path set. On the next update you will get a new rust-analyzer binary though that you would need to removr again.

Unlike vscode, zed has a builtin lsp implementation (yes vscode requires each extension to ship with a separate lsp implementation) and ships with the little bit of glue code to run rust-analyzer. As such it doesn't need you to install a rust-analyzer extension. It does however automatically download rust-analyzer by default if you don't have it installed already.