rank_genes_groups fails to account for multiple comparsions when multiple groups are provided.

Please make sure these conditions are met

[X] I have checked that this issue has not already been reported.
[X] I have confirmed this bug exists on the latest version of scanpy.
[x] (optional) I have confirmed this bug exists on the main branch of scanpy.

What happened?

When running sc.tl.rank_genes_groups, one can provide multiple groups for comparison. However, correction for multiple comparisons are done only within a single pair of group and reference. In other words,

for group2 in perts:
            sc.tl.rank_genes_groups(adata, 
                                    groupby = "gene", 
                                    groups = [group2], 
                                    reference = group1, 
                                    method = 'wilcoxon')

Gives exactly the same p-values as the following:

sc.tl.rank_genes_groups(adata, 
                                    groupby = "gene", 
                                    groups = perts, 
                                    reference = group1, 
                                    method = 'wilcoxon')

To give a bit more context, I am processing Perturb-Seq data from Replogle Cell 2022 paper. I am new to bioinformatics, hence might be missing something. Please let me know whether it is an actual bug or me using the package wrong.

Minimal code sample

import numpy as np
import pandas as pd
import scanpy as sc
from anndata import AnnData

p_value_threshold = 0.05
# Create a minimalistic AnnData object
data = np.random.rand(1000, 5)  # 1000 cells, 5 genes
obs = pd.DataFrame(index=[f'cell{i}' for i in range(1000)])
var = pd.DataFrame(index=[f'gene{i}' for i in range(5)])
adata = AnnData(X=data, obs=obs, var=var)

# Add a 'gene' column to obs to use as groupby
adata.obs['gene'] = np.random.choice(['sample0', 'sample1', 'sample2', 'sample3', 'sample4'], size=1000)

# Define groups
group1 = 'sample0'
perts = ['sample1', 'sample2', 'sample3', 'sample4']

# Run the loop to get p-values
for group2 in perts:
    sc.tl.rank_genes_groups(adata,
                            groupby='gene',
                            groups=[group2],
                            reference=group1,
                            method='wilcoxon')
    result = adata.uns["rank_genes_groups"]
    #mask = result['pvals_adj'][group2] < p_value_threshold
    filtered_genes = result['names'][group2]#[mask]
    filtered_pvals = result['pvals_adj'][group2]#[mask]
    filtered_scores = result['scores'][group2]#[mask]
    print(filtered_pvals)

print('______________________________________________')
# Run all at once
sc.tl.rank_genes_groups(adata,
                        groupby='gene',
                        groups=perts,
                        reference=group1,
                        method='wilcoxon')

result = adata.uns["rank_genes_groups"]
for group2 in perts:
#mask = result['pvals_adj'][group2] < p_value_threshold
    filtered_genes = result['names'][group2]#[mask]
    filtered_pvals = result['pvals_adj'][group2]#[mask]
    filtered_scores = result['scores'][group2]#[mask]
    print(filtered_pvals)

Error output

I would expect to see different adjusted p-values for the first and the second case. When looping (first case) the method does not see other comparisons coming from the loop, while in the second case the method does see them but still does not correct for them.

Versions

``` ----- anndata 0.10.7 scanpy 1.10.2 ----- PIL 10.4.0 anyio NA apport_python_hook NA arrow 1.3.0 asttokens NA attr 23.2.0 attrs 23.2.0 babel 2.14.0 cairo 1.20.1 certifi 2024.07.04 cffi 1.16.0 chardet 4.0.0 charset_normalizer 3.3.2 cloudpickle 3.0.0 colorama 0.4.4 comm 0.2.2 cycler 0.12.1 cython_runtime NA cytoolz 0.12.3 dask 2024.8.0 dateutil 2.9.0.post0 debugpy 1.8.1 decorator 5.1.1 defusedxml 0.7.1 dill 0.3.8 exceptiongroup 1.2.1 executing 2.0.1 fastjsonschema NA fqdn NA gi 3.42.1 gio NA glib NA gobject NA gtk NA h5py 3.11.0 idna 3.3 igraph 0.11.5 ipykernel 6.29.4 isoduration NA jedi 0.19.1 jinja2 3.1.3 joblib 1.4.2 json5 0.9.25 jsonpointer 2.4 jsonschema 4.22.0 jsonschema_specifications NA jupyter_events 0.10.0 jupyter_server 2.14.0 jupyterlab_server 2.27.1 kiwisolver 1.4.5 legacy_api_wrap NA leidenalg 0.10.2 llvmlite 0.42.0 louvain 0.8.2 lz4 4.3.3 markupsafe 2.1.5 matplotlib 3.8.4 more_itertools 8.10.0 mpl_toolkits NA mpmath 1.3.0 natsort 8.4.0 nbformat 5.10.4 netifaces 0.11.0 numba 0.59.1 numexpr 2.10.1 numpy 1.26.4 overrides NA packaging 24.0 pandas 2.2.2 parso 0.8.4 pkg_resources NA platformdirs 4.2.1 plotly 5.22.0 prometheus_client NA prompt_toolkit 3.0.43 psutil 5.9.8 pure_eval 0.2.2 pyarrow 16.0.0 pydev_ipython NA pydevconsole NA pydevd 2.9.5 pydevd_file_utils NA pydevd_plugins NA pydevd_tracing NA pydot 2.0.0 pygments 2.17.2 pyparsing 3.1.2 pythonjsonlogger NA pytz 2022.1 referencing NA requests 2.31.0 rfc3339_validator 0.1.4 rfc3986_validator 0.1.1 rpds NA scipy 1.13.0 send2trash NA session_info 1.0.0 sitecustomize NA six 1.16.0 sklearn 1.4.2 sniffio 1.3.1 socks 1.7.1 stack_data 0.6.3 sympy 1.12 tblib 3.0.0 texttable 1.7.0 threadpoolctl 3.5.0 tlz 0.12.3 toolz 0.12.1 torch 2.1.2+cu121 torchgen NA tornado 6.4 tqdm 4.66.4 traitlets 5.14.3 typing_extensions NA tzdata 2024.1 uri_template NA urllib3 2.2.1 wcwidth 0.2.13 webcolors 1.13 websocket 1.8.0 xxhash NA yaml 5.4.1 zipp NA zmq 26.0.3 zoneinfo NA ----- IPython 8.24.0 jupyter_client 8.6.1 jupyter_core 5.7.2 jupyterlab 4.2.3 notebook 7.2.0 ----- Python 3.10.12 (main, Jul 29 2024, 16:56:48) [GCC 11.4.0] Linux-6.5.0-1027-oem-x86_64-with-glibc2.35 ----- Session information updated at 2024-09-02 14:19 ```

scverse / scanpy