[BUG] peerDependencies resolve only latest versions ignoring semver compatibility with other peer deps

Is there an existing issue for this?

• I have searched the existing issues

This issue exists in the latest npm version

• I am using the latest npm

Current Behavior

We are installing (without --legacy-peer-deps flag) parent module, who wants dependencies child-peer and child-dep. Child-peer has peerDependency for history >=4, child-dep has dependency for history ^4.
npm resolves in the root node_modules 5th major of history, but semver allows us to get 4th major and install it only once for all of them instead installing 5th for root and child-peer; 4th for child-dep.

It is separated behavior for docs advice to make deps versions as broad as possible.

Resolved tree:
└- [parent] history: 5.3.0
└- [child-dep] history: 4.10.1

Dependencies tree:
└- [child-peer] history: devDependencies ^4
└- [child-peer] history: peerDependencies >=4
└- [child-dep] history: dependencies ^4
└- [child-dep] history: peerDependencies ^4

Expected Behavior

Resolved tree:
└- [parent] history: 4.10.1

Dependencies tree:
└- [child-peer] history: devDependencies ^4
└- [child-peer] history: peerDependencies >=4
└- [child-dep] history: dependencies ^4
└- [child-dep] history: peerDependencies ^4

Steps To Reproduce

We have these package.json:

• parent:
  { "name": "parent", "version": "0.0.1", "dependencies": { "child-peer": "0.0.1", "child-dep": "0.0.1" } }
• child-dep:
  { "name": "child-dep", "version": "0.0.1", "dependencies": { "history": "^4" }, "peerDependencies": { "history": "^4" } }
• child-peer:
  { "name": "child-peer", "version": "0.0.1", "peerDependencies": { "history": ">=4" }, "devDependencies": { "history": "^4" } }

Install parent. Look at parent/node_modules/history version. No 4th major, but 5th major.

Environment

• npm: 8.5.3
• Node.js: 16.14.0
• OS Name: macOS 12.4
• System Model Name: Macbook Pro
• npm config: Sorry, there is my own creds

Reproduce the issue using the parent, child-peer, and child-dep package.json fixtures and the npm 8.5.3 environment described. Compare the installed history version with the expected dependency tree; done means compatible history 4.x is resolved once without requiring --legacy-peer-deps.