Put functional tests in tests/functional

I think it is bad for these reasons when `tests/` contains a mix of
functional and integration tests

 - Concepts is harder to understand, the documentation makes a good
   unit vs functional vs integration distinction, but when the
   integration tests are just two subdirs within `tests/` this is not
   clear.

 - Source filtering in the `flake.nix` is more complex. We need to
   filter out some of the dirs from `tests/`, rather than simply pick
   the dirs we want and take all of them. This is a good sign the
   structure of what we are trying to do is not matching the structure
   of the files.

With this change we have a clean:
```shell-session
$ git show 'HEAD:tests'
tree HEAD:tests

functional/
installer/
nixos/
```

(cherry picked from commit 68c81c7375)

tests/functional/flakes/init.sh

@@ -0,0 +1,87 @@
+source ./common.sh
+
+requireGit
+
+templatesDir=$TEST_ROOT/templates
+flakeDir=$TEST_ROOT/flake
+nixpkgsDir=$TEST_ROOT/nixpkgs
+
+nix registry add --registry $registry templates git+file://$templatesDir
+nix registry add --registry $registry nixpkgs git+file://$nixpkgsDir
+
+createGitRepo $nixpkgsDir
+createSimpleGitFlake $nixpkgsDir
+
+# Test 'nix flake init'.
+createGitRepo $templatesDir
+
+cat > $templatesDir/flake.nix <<EOF
+{
+  description = "Some templates";
+
+  outputs = { self }: {
+    templates = rec {
+      trivial = {
+        path = ./trivial;
+        description = "A trivial flake";
+        welcomeText = ''
+            Welcome to my trivial flake
+        '';
+      };
+      default = trivial;
+    };
+  };
+}
+EOF
+
+mkdir $templatesDir/trivial
+
+cat > $templatesDir/trivial/flake.nix <<EOF
+{
+  description = "A flake for building Hello World";
+
+  outputs = { self, nixpkgs }: {
+    packages.$system = rec {
+      hello = nixpkgs.legacyPackages.$system.hello;
+      default = hello;
+    };
+  };
+}
+EOF
+echo a > $templatesDir/trivial/a
+echo b > $templatesDir/trivial/b
+
+git -C $templatesDir add flake.nix trivial/
+git -C $templatesDir commit -m 'Initial'
+
+nix flake check templates
+nix flake show templates
+nix flake show templates --json | jq
+
+createGitRepo $flakeDir
+(cd $flakeDir && nix flake init)
+(cd $flakeDir && nix flake init) # check idempotence
+git -C $flakeDir add flake.nix
+nix flake check $flakeDir
+nix flake show $flakeDir
+nix flake show $flakeDir --json | jq
+git -C $flakeDir commit -a -m 'Initial'
+
+# Test 'nix flake init' with benign conflicts
+createGitRepo "$flakeDir"
+echo a > $flakeDir/a
+(cd $flakeDir && nix flake init) # check idempotence
+
+# Test 'nix flake init' with conflicts
+createGitRepo "$flakeDir"
+echo b > $flakeDir/a
+pushd $flakeDir
+(! nix flake init) |& grep "refusing to overwrite existing file '$flakeDir/a'"
+popd
+git -C $flakeDir commit -a -m 'Changed'
+
+# Test 'nix flake new'.
+rm -rf $flakeDir
+nix flake new -t templates#trivial $flakeDir
+nix flake new -t templates#trivial $flakeDir # check idempotence
+nix flake check $flakeDir