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/
```

tests/functional/init.sh

@@ -0,0 +1,41 @@
+# Don't start the daemon
+source common/vars-and-functions.sh
+
+test -n "$TEST_ROOT"
+if test -d "$TEST_ROOT"; then
+    chmod -R u+w "$TEST_ROOT"
+    # We would delete any daemon socket, so let's stop the daemon first.
+    killDaemon
+    rm -rf "$TEST_ROOT"
+fi
+mkdir "$TEST_ROOT"
+
+mkdir "$NIX_STORE_DIR"
+mkdir "$NIX_LOCALSTATE_DIR"
+mkdir -p "$NIX_LOG_DIR"/drvs
+mkdir "$NIX_STATE_DIR"
+mkdir "$NIX_CONF_DIR"
+
+cat > "$NIX_CONF_DIR"/nix.conf <<EOF
+build-users-group =
+keep-derivations = false
+sandbox = false
+experimental-features = nix-command flakes
+gc-reserved-space = 0
+substituters =
+flake-registry = $TEST_ROOT/registry.json
+show-trace = true
+include nix.conf.extra
+trusted-users = $(whoami)
+EOF
+
+cat > "$NIX_CONF_DIR"/nix.conf.extra <<EOF
+fsync-metadata = false
+!include nix.conf.extra.not-there
+EOF
+
+# Initialise the database.
+nix-store --init
+
+# Did anything happen?
+test -e "$NIX_STATE_DIR"/db/db.sqlite