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/check.sh

@@ -0,0 +1,91 @@
+source common.sh
+
+# XXX: This shouldn’t be, but #4813 cause this test to fail
+buggyNeedLocalStore "see #4813"
+
+checkBuildTempDirRemoved ()
+{
+    buildDir=$(sed -n 's/CHECK_TMPDIR=//p' $1 | head -1)
+    checkBuildIdFile=${buildDir}/checkBuildId
+    [[ ! -f $checkBuildIdFile ]] || ! grep $checkBuildId $checkBuildIdFile
+}
+
+# written to build temp directories to verify created by this instance
+checkBuildId=$(date +%s%N)
+
+clearStore
+
+nix-build dependencies.nix --no-out-link
+nix-build dependencies.nix --no-out-link --check
+
+# Build failure exit codes (100, 104, etc.) are from
+# doc/manual/src/command-ref/status-build-failure.md
+
+# check for dangling temporary build directories
+# only retain if build fails and --keep-failed is specified, or...
+# ...build is non-deterministic and --check and --keep-failed are both specified
+nix-build check.nix -A failed --argstr checkBuildId $checkBuildId \
+    --no-out-link 2> $TEST_ROOT/log || status=$?
+[ "$status" = "100" ]
+checkBuildTempDirRemoved $TEST_ROOT/log
+
+nix-build check.nix -A failed --argstr checkBuildId $checkBuildId \
+    --no-out-link --keep-failed 2> $TEST_ROOT/log || status=$?
+[ "$status" = "100" ]
+if checkBuildTempDirRemoved $TEST_ROOT/log; then false; fi
+
+nix-build check.nix -A deterministic --argstr checkBuildId $checkBuildId \
+    --no-out-link 2> $TEST_ROOT/log
+checkBuildTempDirRemoved $TEST_ROOT/log
+
+nix-build check.nix -A deterministic --argstr checkBuildId $checkBuildId \
+    --no-out-link --check --keep-failed 2> $TEST_ROOT/log
+if grepQuiet 'may not be deterministic' $TEST_ROOT/log; then false; fi
+checkBuildTempDirRemoved $TEST_ROOT/log
+
+nix-build check.nix -A nondeterministic --argstr checkBuildId $checkBuildId \
+    --no-out-link 2> $TEST_ROOT/log
+checkBuildTempDirRemoved $TEST_ROOT/log
+
+nix-build check.nix -A nondeterministic --argstr checkBuildId $checkBuildId \
+    --no-out-link --check 2> $TEST_ROOT/log || status=$?
+grep 'may not be deterministic' $TEST_ROOT/log
+[ "$status" = "104" ]
+checkBuildTempDirRemoved $TEST_ROOT/log
+
+nix-build check.nix -A nondeterministic --argstr checkBuildId $checkBuildId \
+    --no-out-link --check --keep-failed 2> $TEST_ROOT/log || status=$?
+grep 'may not be deterministic' $TEST_ROOT/log
+[ "$status" = "104" ]
+if checkBuildTempDirRemoved $TEST_ROOT/log; then false; fi
+
+clearStore
+
+path=$(nix-build check.nix -A fetchurl --no-out-link)
+
+chmod +w $path
+echo foo > $path
+chmod -w $path
+
+nix-build check.nix -A fetchurl --no-out-link --check
+# Note: "check" doesn't repair anything, it just compares to the hash stored in the database.
+[[ $(cat $path) = foo ]]
+
+nix-build check.nix -A fetchurl --no-out-link --repair
+[[ $(cat $path) != foo ]]
+
+echo 'Hello World' > $TEST_ROOT/dummy
+nix-build check.nix -A hashmismatch --no-out-link || status=$?
+[ "$status" = "102" ]
+
+echo -n > $TEST_ROOT/dummy
+nix-build check.nix -A hashmismatch --no-out-link
+echo 'Hello World' > $TEST_ROOT/dummy
+
+nix-build check.nix -A hashmismatch --no-out-link --check || status=$?
+[ "$status" = "102" ]
+
+# Multiple failures with --keep-going
+nix-build check.nix -A nondeterministic --no-out-link
+nix-build check.nix -A nondeterministic -A hashmismatch --no-out-link --check --keep-going || status=$?
+[ "$status" = "110" ]