Step 1: Identify the relevant industry
Naturgy Energy Group S.A. operates in the energy sector, specifically in gas and electricity distribution and generation. The provided industry methodologies include "Regulated Utilities", "Oil And Gas Exploration And Production", "Unregulated Power And Gas", and "Transportation Infrastructure". Naturgy has a mix of regulated and unregulated operations but is primarily known as a regulated utility. However, for the purpose of calculating financial metrics (Adjusted EBITDA, FFO, Adjusted Debt), the methodology refers to the general corporate baseline formulas, which apply across the board for the ratio calculations. We will use the baseline formulas specified in the task.

Step 2: Estimate 2021 Adjusted EBITDA
Formula: Adjusted_EBITDA = EBITDA (reported) + adjustment_leases + nonrecurring_losses - nonrecurring_gains ± pension_adjustments ± joint_venture_proportional_EBITDA ± other_normalization_adjustments
From the facts, "Beneficio Bruto De Explotacion Ebitda" for 2021-01-01 to 2022-01-01 is 3,529,000,000 EUR. 
There are no explicit adjustments for leases, pensions, or nonrecurring items in the data. We note "Other Gains Losses" of 133,000,000 EUR, which could be non-recurring gains, but typically S&P adjustments require specific disclosure. Without specific nonrecurring or lease adjustment data, we use the reported EBITDA.
Adjusted_EBITDA 2021 = 3,529,000,000 EUR.

Step 3: Estimate 2021 FFO
Formula: FFO = Adjusted_EBITDA - cash_interest - cash_taxes
From the facts for 2021:
- Cash interest (Interest Paid Classified As Operating Activities) = 488,000,000 EUR.
- Cash taxes (Income Taxes Paid Classified As Operating Activities) = 864,000,000 EUR.
FFO 2021 = 3,529,000,000 - 488,000,000 - 864,000,000 = 2,177,000,000 EUR.

Step 4: Estimate 2021 Adjusted Debt
Formula: Adjusted_Debt = (reported_debt + leases + pension_deficit + guarantees + hybrid_debt_portion + other_debt_like_items) - eligible_cash
From the facts for 2022-01-01:
- Reported debt = Longterm Borrowings (13,786,000,000) + Current Borrowings And Current Portion Of Noncurrent Borrowings (1,493,000,000) = 15,279,000,000 EUR.
- Lease liabilities = Noncurrent Lease Liabilities (1,325,000,000) + Current Lease Liabilities (196,000,000) = 1,521,000,000 EUR.
- Other debt-like items = Pasivo Derivados Comerciales No Corriente (730,000,000) + Pasivo Derivados Comerciales Corriente (2,704,000,000) = 3,434,000,000 EUR. (Derivatives liabilities with negative fair value are often treated as debt-like).
- Eligible cash = Cash And Cash Equivalents = 3,965,000,000 EUR. (Assuming most cash is eligible given typical utility liquidity profiles).
Adjusted_Debt 2021 = 15,279,000,000 + 1,521,000,000 + 3,434,000,000 - 3,965,000,000 = 16,269,000,000 EUR.

Step 5: Calculate 2021 Adjusted Debt / Adjusted EBITDA
Ratio 2021 = 16,269,000,000 / 3,529,000,000 = 4.61x

Step 6: Calculate 2021 FFO / Adjusted Debt
Ratio 2021 = 2,177,000,000 / 16,269,000,000 = 0.1338 (or 13.38%)

Step 7: Estimate 2022 Adjusted EBITDA
From the facts, "Beneficio Bruto De Explotacion Ebitda" for 2022-01-01 to 2023-01-01 is 4,954,000,000 EUR.
Adjusted_EBITDA 2022 = 4,954,000,000 EUR.

Step 8: Estimate 2022 FFO
From the facts for 2022:
- Cash interest = 520,000,000 EUR.
- Cash taxes = 762,000,000 EUR.
FFO 2022 = 4,954,000,000 - 520,000,000 - 762,000,000 = 3,672,000,000 EUR.

Step 9: Estimate 2022 Adjusted Debt
From the facts for 2023-01-01:
- Reported debt = Longterm Borrowings (12,689,000,000) + Current Borrowings And Current Portion Of Noncurrent Borrowings (2,110,000,000) = 14,799,000,000 EUR.
- Lease liabilities = Noncurrent Lease Liabilities (1,309,000,000) + Current Lease Liabilities (177,000,000) = 1,486,000,000 EUR.
- Other debt-like items = Pasivo Derivados Comerciales No Corriente (1,664,000,000) + Pasivo Derivados Comerciales Corriente (1,624,000,000) = 3,288,000,000 EUR.
- Eligible cash = Cash And Cash Equivalents = 3,985,000,000 EUR.
Adjusted_Debt 2022 = 14,799,000,000 + 1,486,000,000 + 3,288,000,000 - 3,985,000,000 = 15,588,000,000 EUR.

Step 10: Calculate 2022 Adjusted Debt / Adjusted EBITDA
Ratio 2022 = 15,588,000,000 / 4,954,000,000 = 3.15x

Step 11: Calculate 2022 FFO / Adjusted Debt
Ratio 2022 = 3,672,000,000 / 15,588,000,000 = 0.2356 (or 23.56%)

Step 12: Classify the year-on-year credit trend
Signal 1: Leverage (Change in Adjusted Debt / EBITDA)
Change = 3.15x - 4.61x = -1.46x. 
The change is ≤ -0.2x, which indicates "Improving".

Signal 2: Cash-flow coverage (Change in FFO / Adjusted Debt)
Change = 0.2356 - 0.1338 = 0.1018 (or 10.18 percentage points).
The change is ≥ +0.03, which indicates "Improving".

Combining the signals:
Both Signal 1 and Signal 2 agree on "Improving". Leverage decreased significantly due to higher EBITDA and lower adjusted debt, and cash flow coverage increased substantially due to higher FFO generation against a lower debt base.

<answer>Improving</answer>