test: AMM TXE tests (#16458)

Fixes #10289

Just like my [other recent
PR](#16451) decided
to add TXE tests for AMM.

## On using AI here
The only thing I did manually here is to merge a few test cases because
they were too long-running as setting up the initial state is costly. I
also told it to not have precise ratio in the second call to
`add_liquidity` to test the refund. Other than this AI pretty much
managed to nail it.

### Update on AI
Code quality was not great and had to redo quite a lot of stuff. That
could be improved though if we had a proper reference (plenty of the
style issues were present in the rest of our codebase).

Author: benesjan

noir-projects/noir-contracts/contracts/app/amm_contract/src/main.nr

@@ -1,5 +1,6 @@
 mod lib;
 mod config;
+mod test;
 
 use dep::aztec::macros::aztec;
 
@@ -54,9 +55,9 @@ pub contract AMM {
 
     /// Amount of liquidity which gets locked when liquidity is provided for the first time. Its purpose is to prevent
     /// the pool from ever emptying which could lead to undefined behavior.
-    global MINIMUM_LIQUIDITY: u128 = 1000;
+    pub global MINIMUM_LIQUIDITY: u128 = 1000;
     /// We set it to 99 times the minimum liquidity. That way the first LP gets 99% of the value of their deposit.
-    global INITIAL_LIQUIDITY: u128 = 99000;
+    pub global INITIAL_LIQUIDITY: u128 = 99000;
 
     // TODO(#9480): Either deploy the liquidity contract in the constructor or verify it that it corresponds to what
     // this contract expects (i.e. that the AMM has permission to mint and burn).

noir-projects/noir-contracts/contracts/app/amm_contract/src/test/mod.nr

@@ -0,0 +1,2 @@
+mod test;
+pub(crate) mod utils;