Following @orlp's approach, I would pivot as suggested, create a full combination, and then use the .select() method to filter the columns.

import polars as pl
import itertools

df = pl.DataFrame({
    "id": [1, 2, 3, 1, 2, 3, 1, 2, 3],
    "variable": ["x1", "x1", "x1", "x2", "x2", "x2", "x3", "x3", "x3"],
    "favorite": ["APP", "APP", "WEB", "APP", "WEB", "APP", "APP", "APP", "WEB"]
})

action_through_app = (
    df
    .with_columns(pl.col.favorite == "APP")
    .pivot(index="id", on="variable", values="favorite")
)

all_combinations = []

states = df["variable"].unique().to_list()
for r in range(1,len(states)+1):
    all_combinations.extend(itertools.combinations(states, r))

def test_f(df):
    return(
        df.with_columns((pl.sum_horizontal(pl.all()) >= 0.6*pl.sum_horizontal(pl.all().is_not_null())).alias("target"))
    )

new_rows = []

for i in range(len(all_combinations)):
    df_filtered = action_through_app.select(all_combinations[i])
    df_test = test_f(df_filtered).select(pl.col("target").sum()).to_series().to_list()
    x = df_test[0]
    new_rows.append({"loop_index": i, "size": x})
    
df_final = pl.DataFrame(new_rows)

This way i have this output:

shape: (7, 2)
┌────────────┬──────┐
│ loop_index ┆ size │
│ ---        ┆ ---  │
│ i64        ┆ i64  │
╞════════════╪══════╡
│ 0          ┆ 2    │
│ 1          ┆ 2    │
│ 2          ┆ 2    │
│ 3          ┆ 1    │
│ 4          ┆ 2    │
│ 5          ┆ 1    │
│ 6          ┆ 2    │
└────────────┴──────┘