What it's all about

Right now, termux-exec only wraps execve.
env however, uses execvp to execute external programs.
https://github.com/coreutils/coreutils/blob/a94a551ee031e0ff07d707f867cb08a8be83e78c/src/env.c#L921

The man for exec(3) does say that:

The exec() family of functions replaces the current process image with a new process image. The functions described in this manual page are layered on top of execve(2).

However, it refers to execve as a system call, not as a library function.

What's broken

Here's a simple test to show inconsistency between ./test.sh and env ./test.sh

That should not happen.
On my system, /bin/sh leads to /system/bin/sh.
It shows that the parameters passed to execvp are not altered.