Windows Miniforge Prompt loses system PATH (System32 missing) when using `Scripts\activate.bat` (mamba activate)

### Solution to issue cannot be found in the documentation.

- [x] I checked the documentation.

### Issue

#### Summary
On Windows, launching a Miniforge Prompt via `Scripts\activate.bat` results in `PATH` being overwritten to only Miniforge directories, dropping system paths (e.g. `%SystemRoot%\System32`). As a consequence, standard commands like `where` (and also `code` from VS Code) are not found.

Using `conda activate` (via `conda_hook.bat`) instead of `mamba activate` fixes the issue.

#### How I launch the prompt
Custom shortcut target (similar to the Start Menu Miniforge Prompt):

```

%windir%\system32\cmd.exe "/K" C:\Users\miniforge3\Scripts\activate.bat C:\Users\miniforge3

```

#### Steps to reproduce
1. Install Miniforge3 on Windows.
2. Launch Miniforge Prompt (or use the shortcut above).
3. In the opened `cmd.exe` (base env), run:

```

echo %PATH%
echo %SystemRoot%
where where
code --version

```

#### Expected behavior
- `PATH` should still contain system directories such as:
- `%SystemRoot%\System32`
- `%SystemRoot%`
- `%SystemRoot%\System32\Wbem`
- etc.
- `where` should work.
- `code` should work (if VS Code CLI is installed / on PATH in the parent environment).

#### Actual behavior
- `PATH` becomes only Miniforge paths (system paths are missing). Example:

```

C:\Users\miniforge3;C:\Users\miniforge3\Library\mingw-w64\bin;C:\Users\miniforge3\Library\usr\bin;C:\Users\miniforge3\Library\bin;C:\Users\miniforge3\Scripts;C:\Users\miniforge3\bin;C:\Users\miniforge3\condabin

```

- `where` is not recognized:

```

'where' is not recognized as an internal or external command,
operable program or batch file.

````

- `code` is also not recognized in this prompt, while it works in cmd or PowerShell (`code --version` prints a version normally).

#### Workaround / Fix
Editing `C:\Users\\miniforge3\Scripts\activate.bat` to use `conda activate` instead of `mamba activate` fixes it.

before `activate.bat`:

```bat
@REM Copyright (C) 2021 QuantStack
@REM SPDX-License-Identifier: BSD-3-Clause

@CALL "%~dp0..\condabin\mamba_hook.bat"
mamba activate %*
````

Current modified `activate.bat`:

```bat
@REM Copyright (C) 2021 QuantStack
@REM SPDX-License-Identifier: BSD-3-Clause

@CALL "%~dp0..\condabin\conda_hook.bat"
conda activate %*
````

After this change, `PATH` keeps system entries and both `where` and `code` work.

#### Additional info / suspicion

It looks like the `mamba_hook.bat` / `mamba activate` path setup on Windows may be reconstructing `PATH` without preserving the original process `PATH` inherited from the parent shell, resulting in system paths being dropped.

#### Environment

(base) C:\Users\>mamba --version
2.4.0
(base) C:\Users\>conda --version
conda 25.11.0

### Installed packages

```shell
# Name Version Build Channel
archspec 0.2.5 pyhd8ed1ab_0 conda-forge
boltons 25.0.0 pyhd8ed1ab_0 conda-forge
brotli-python 1.2.0 py312hc6d9e41_1 conda-forge
bzip2 1.0.8 h0ad9c76_8 conda-forge
ca-certificates 2025.11.12 h4c7d964_0 conda-forge
certifi 2025.11.12 pyhd8ed1ab_0 conda-forge
cffi 2.0.0 py312he06e257_1 conda-forge
charset-normalizer 3.4.4 pyhd8ed1ab_0 conda-forge
colorama 0.4.6 pyhd8ed1ab_1 conda-forge
conda 25.11.0 py312h2e8e312_0 conda-forge
conda-libmamba-solver 25.11.0 pyhd8ed1ab_0 conda-forge
conda-package-handling 2.4.0 pyh7900ff3_2 conda-forge
conda-package-streaming 0.12.0 pyhd8ed1ab_0 conda-forge
cpp-expected 1.3.1 h477610d_0 conda-forge
distro 1.9.0 pyhd8ed1ab_1 conda-forge
fmt 12.0.0 h29169d4_0 conda-forge
frozendict 2.4.7 py312he06e257_0 conda-forge
h2 4.3.0 pyhcf101f3_0 conda-forge
hpack 4.1.0 pyhd8ed1ab_0 conda-forge
hyperframe 6.1.0 pyhd8ed1ab_0 conda-forge
idna 3.11 pyhd8ed1ab_0 conda-forge
jsonpatch 1.33 pyhd8ed1ab_1 conda-forge
jsonpointer 3.0.0 py312h2e8e312_2 conda-forge
krb5 1.21.3 hdf4eb48_0 conda-forge
libarchive 3.8.2 gpl_h26aea39_100 conda-forge
libcurl 8.17.0 h43ecb02_0 conda-forge
libexpat 2.7.3 hac47afa_0 conda-forge
libffi 3.5.2 h52bdfb6_0 conda-forge
libiconv 1.18 hc1393d2_2 conda-forge
liblzma 5.8.1 h2466b09_2 conda-forge
libmamba 2.4.0 h3f46830_1 conda-forge
libmambapy 2.4.0 py312h6891394_1 conda-forge
libsolv 0.7.35 h8883371_0 conda-forge
libsqlite 3.51.1 hf5d6505_0 conda-forge
libssh2 1.11.1 h9aa295b_0 conda-forge
libxml2 2.15.1 h5d26750_0 conda-forge
libxml2-16 2.15.1 h692994f_0 conda-forge
libzlib 1.3.1 h2466b09_2 conda-forge
lz4-c 1.10.0 h2466b09_1 conda-forge
lzo 2.10 h6a83c73_1002 conda-forge
mamba 2.4.0 h794742e_1 conda-forge
menuinst 2.4.1 py312hbb81ca0_0 conda-forge
miniforge_console_shortcut 1.0 h57928b3_0 conda-forge
msgpack-python 1.1.2 py312hf90b1b7_1 conda-forge
nlohmann_json-abi 3.12.0 h0f90c79_1 conda-forge
nodejs 25.2.1 he453025_1 conda-forge
openssl 3.6.0 h725018a_0 conda-forge
packaging 25.0 pyh29332c3_1 conda-forge
pip 25.3 pyh8b19718_0 conda-forge
platformdirs 4.5.0 pyhcf101f3_0 conda-forge
pluggy 1.6.0 pyhf9edf01_1 conda-forge
pybind11-abi 11 hc364b38_1 conda-forge
pycosat 0.6.6 py312he06e257_3 conda-forge
pycparser 2.22 pyh29332c3_1 conda-forge
pysocks 1.7.1 pyh09c184e_7 conda-forge
python 3.12.12 h0159041_1_cpython conda-forge
python_abi 3.12 8_cp312 conda-forge
reproc 14.2.5.post0 h2466b09_0 conda-forge
reproc-cpp 14.2.5.post0 he0c23c2_0 conda-forge
requests 2.32.5 pyhd8ed1ab_0 conda-forge
ruamel.yaml 0.18.16 py312he06e257_0 conda-forge
ruamel.yaml.clib 0.2.14 py312he06e257_0 conda-forge
setuptools 80.9.0 pyhff2d567_0 conda-forge
simdjson 4.2.2 h49e36cd_0 conda-forge
tk 8.6.13 h2c6b04d_3 conda-forge
tqdm 4.67.1 pyhd8ed1ab_1 conda-forge
truststore 0.10.3 pyhe01879c_0 conda-forge
tzdata 2025b h78e105d_0 conda-forge
ucrt 10.0.26100.0 h57928b3_0 conda-forge
urllib3 2.5.0 pyhd8ed1ab_0 conda-forge
vc 14.3 h2b53caa_32 conda-forge
vc14_runtime 14.44.35208 h818238b_32 conda-forge
vcomp14 14.44.35208 h818238b_32 conda-forge
wheel 0.45.1 pyhd8ed1ab_1 conda-forge
win_inet_pton 1.1.0 pyh7428d3b_8 conda-forge
yaml-cpp 0.8.0 he0c23c2_0 conda-forge
zstandard 0.25.0 py312he5662c2_1 conda-forge
zstd 1.5.7 h534d264_6 conda-forge
```

### Environment info

```shell
active environment : base
active env location : C:\Users\\miniforge3
shell level : 1
user config file : C:\Users\\.condarc
populated config files : C:\Users\\miniforge3\.condarc
conda version : 25.11.0
conda-build version : not installed
python version : 3.12.12.final.0
solver : libmamba (default)
virtual packages : __archspec=1=skylake
__conda=25.11.0=0
__cuda=0=0
__win=10.0.26200=0
base environment : C:\Users\\miniforge3 (writable)
conda av data dir : C:\Users\\miniforge3\etc\conda
conda av metadata url : None
channel URLs : https://conda.anaconda.org/conda-forge/win-64
https://conda.anaconda.org/conda-forge/noarch
package cache : C:\Users\\miniforge3\pkgs
C:\Users\\.conda\pkgs
C:\Users\\AppData\Local\conda\conda\pkgs
envs directories : C:\Users\\miniforge3\envs
C:\Users\\.conda\envs
C:
```