clang++ cannot find iostream

Here is a simple code :

#include <iostream>
#include <algorithm>
#include <vector>
#include <functional>
#include <iterator>
#include <iomanip>
#include <cmath>

int main()
{
    std::cout << "Hello, world!" << std::endl;
    return 0;
}

when I want to compile it with g++, there is no issue :

$ g++ test.cpp 
$ ./a.out 
Hello, world!

but if I want to do it with clang++ it doesn't work anymore :

$ clang++ t.cpp               
t.cpp:1:10: fatal error: 'iostream' file not found
#include <iostream>
         ^~~~~~~~~~
1 error generated.

Here is what returns clang if I add the -v option :

$ clang++ test.cpp -v
Ubuntu clang version 14.0.0-1ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin
Found candidate GCC installation: /usr/bin/../lib/gcc/x86_64-linux-gnu/11
Found candidate GCC installation: /usr/bin/../lib/gcc/x86_64-linux-gnu/12
Found candidate GCC installation: /usr/bin/../lib/gcc/x86_64-linux-gnu/9
Selected GCC installation: /usr/bin/../lib/gcc/x86_64-linux-gnu/12
Candidate multilib: .;@m64
Selected multilib: .;@m64
Found CUDA installation: /usr/local/cuda, version 
 "/usr/lib/llvm-14/bin/clang" -cc1 -triple x86_64-pc-linux-gnu -emit-obj -mrelax-all --mrelax-relocations -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name test.cpp -mrelocation-model pic -pic-level 2 -pic-is-pie -mframe-pointer=all -fmath-errno -ffp-contract=on -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -mllvm -treat-scalable-fixed-error-as-warning -debugger-tuning=gdb -v -fcoverage-compilation-dir=/home/saigre/Bureau -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -internal-isystem /usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++ -internal-isystem /usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/x86_64-linux-gnu -internal-isystem /usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/backward -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -fdeprecated-macro -fdebug-compilation-dir=/home/saigre/Bureau -ferror-limit 19 -fgnuc-version=4.2.1 -fcxx-exceptions -fexceptions -fcolor-diagnostics -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/test-e9d03e.o -x c++ test.cpp
clang -cc1 version 14.0.0 based upon LLVM 14.0.0 default target x86_64-pc-linux-gnu
ignoring nonexistent directory "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/x86_64-linux-gnu"
ignoring nonexistent directory "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/backward"
ignoring nonexistent directory "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../x86_64-linux-gnu/include"
ignoring nonexistent directory "/include"
#include "..." search starts here:
#include <...> search starts here:
 /usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++
 /usr/lib/llvm-14/lib/clang/14.0.0/include
 /usr/local/include
 /usr/include/x86_64-linux-gnu
 /usr/include
End of search list.
test.cpp:1:10: fatal error: 'iostream' file not found
#include <iostream>
         ^~~~~~~~~~
1 error generated.

This issue seems to be identical to this post, but no solution from it worked from me. I also found this topic who proposed this solution

clang++ -I/usr/include/c++/11 -I/usr/include/x86_64-linux-gnu/c++/11 -L /usr/lib/gcc/x86_64-linux-gnu/11 test.cpp

working fine. But I have an application that, during its execution compiles a small cpp script using clang and I don't have a hand on the options I can pass to it.

Is there a way to fix the configuration of clang, such that the command clang++ test.cpp works without adding any option ? (it did work in the past)

I'm using ubuntu 22.04, and gcc-12.