chore: Add circuit input checks to bootstrap.sh (#11261)

This pulls across the tests which are in earthly so they exist in
bootstrap.sh as well


https://github.com/AztecProtocol/aztec-packages/blob/642bce68a3e0eea29fa3ebb8c11cf4af02fe992b/noir-projects/Earthfile#L13-L17

There's a small amount of duplication here as it seems like `bootstrap
test` doesn't make use of `bootstrap test-cmds` in this package. I'm not
sure what's up so I'm doing light touches.

noir-projects/noir-protocol-circuits/bootstrap.sh

@@ -138,6 +138,9 @@ function build {
   return $code
 }
 
+# We don't blindly execute all circuits as some will have no `Prover.toml`.
+CIRCUITS_TO_EXECUTE="private-kernel-init private-kernel-inner private-kernel-reset private-kernel-tail-to-public private-kernel-tail rollup-base-private rollup-base-public rollup-block-root rollup-block-merge rollup-merge rollup-root"
+
 function test {
   set -eu
   name=$(basename "$PWD")
@@ -146,6 +149,10 @@ function test {
 
   RAYON_NUM_THREADS= $NARGO test --skip-brillig-constraints-check
   cache_upload_flag $name-tests-$CIRCUITS_HASH
+
+  for circuit in $CIRCUITS_TO_EXECUTE; do
+    $NARGO execute --program-dir noir-projects/noir-protocol-circuits/crates/$circuit --silence-warnings --skip-brillig-constraints-check
+  done
 }
 
 export -f compile test build
@@ -171,6 +178,9 @@ case "$CMD" in
     $NARGO test --list-tests --silence-warnings | while read -r package test; do
       echo "noir-projects/scripts/run_test.sh noir-protocol-circuits $package $test"
     done
+    for circuit in $CIRCUITS_TO_EXECUTE; do
+      echo "$NARGO execute --program-dir noir-projects/noir-protocol-circuits/crates/$circuit --silence-warnings --skip-brillig-constraints-check"
+    done
     ;;
   "ci")
     parallel --tag --line-buffered {} ::: build test