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/test-infra.sh

@@ -0,0 +1,85 @@
+# Test the functions for testing themselves!
+# Also test some assumptions on how bash works that they rely on.
+source common.sh
+
+# `true` should exit with 0
+expect 0 true
+
+# `false` should exit with 1
+expect 1 false
+
+# `expect` will fail when we get it wrong
+expect 1 expect 0 false
+
+noisyTrue () {
+    echo YAY! >&2
+    true
+}
+
+noisyFalse () {
+    echo NAY! >&2
+    false
+}
+
+# These should redirect standard error to standard output
+expectStderr 0 noisyTrue | grepQuiet YAY
+expectStderr 1 noisyFalse | grepQuiet NAY
+
+# `set -o pipefile` is enabled
+
+pipefailure () {
+    # shellcheck disable=SC2216
+    true | false | true
+}
+expect 1 pipefailure
+unset pipefailure
+
+pipefailure () {
+    # shellcheck disable=SC2216
+    false | true | true
+}
+expect 1 pipefailure
+unset pipefailure
+
+commandSubstitutionPipeFailure () {
+    # shellcheck disable=SC2216
+    res=$(set -eu -o pipefail; false | true | echo 0)
+}
+expect 1 commandSubstitutionPipeFailure
+
+# `set -u` is enabled
+
+# note (...), making function use subshell, as unbound variable errors
+# in the outer shell are *rightly* not recoverable.
+useUnbound () (
+    set -eu
+    # shellcheck disable=SC2154
+    echo "$thisVariableIsNotBound"
+)
+expect 1 useUnbound
+
+# ! alone unfortunately negates `set -e`, but it works in functions:
+# shellcheck disable=SC2251
+! true
+funBang () {
+    ! true
+}
+expect 1 funBang
+unset funBang
+
+# `grep -v -q` is not what we want for exit codes, but `grepInverse` is
+# Avoid `grep -v -q`. The following line proves the point, and if it fails,
+# we'll know that `grep` had a breaking change or `-v -q` may not be portable.
+{ echo foo; echo bar; } | grep -v -q foo
+{ echo foo; echo bar; } | expect 1 grepInverse foo
+
+# `grepQuiet` is quiet
+res=$(set -eu -o pipefail; echo foo | grepQuiet foo | wc -c)
+(( res == 0 ))
+unset res
+
+# `greqQietInverse` is both
+{ echo foo; echo bar; } | expect 1 grepQuietInverse foo
+res=$(set -eu -o pipefail; echo foo | expect 1 grepQuietInverse foo | wc -c)
+(( res == 0 ))
+unset res