[Mohammad Sohail Shaikh (sohailshk)]

Why are these changes needed?

LGBMEstimator.fit() (inherited by RandomForestEstimator and ExtraTreesEstimator) caps the iteration count by the remaining time budget using self._t1, which only exists after the timing fits of a search trial. max_iter < 2 skips the search and retrains the initial config on a fresh estimator with the time budget still set, so:

AutoML().fit(X, y, task="classification", time_budget=5, max_iter=1, estimator_list=["rf"])
# AttributeError: 'RandomForestEstimator' object has no attribute '_t1'

max_iter=0 fails the same way, including the documented zero-shot form max_iter=0, starting_points="data", estimator_list=["rf", "lgbm"], time_budget=60 (all run on main). extra_tree also fails; lgbm, xgboost, xgb_limitdepth, lrl1, sgd, kneighbor are fine. From code reading: the max_iter > 1 path already sets time_budget = -1 before retraining (automl.py), which is why searches never hit this. The fix keeps the configured iteration count when no timing exists.
Tests (rf/extra_tree x max_iter 0/1, plus the zero-shot form): 5 failed on main, 5 pass. test_training_log, test_multiclass, test_regression, test_resampler, test_classification, test_extra_models: 99 passed; failures/error are missing-catboost cases that also fail on main.

Related issue number

none.

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Checks run: black (line length 120) and ruff on the changed files. The pinned pre-commit hook versions were not run. No doc changes are needed.