My condolences.
As others have said, you should receive all of the tax documents for his 2025 in January 2026. You'll get a 1099-SSA for his SS income, and probably two 1099-Rs for the pension and the IRA distribution. You might get some 1099-INTs if he had money in taxable savings accounts. A 1099-B if he had a brokerage account, but it sounds like not.
SS timing is a little weird. Since he lived all of January, he was entitled to his January SS benefit, which would have been paid in February. Usually SS gets this right, especially if they were notified promptly, which is usually done by the funeral home.
You will need to file a normal 1040 for the income he received while he was alive. The main difference is you will also need to note on the tax return by his name that he is deceased and include his date of death. Most tax software like TurboTax can handle this just fine. It is easiest to file electronically and either direct deposit or direct debit from a checking account. If you have an estate account or are keeping an account open with his money in it, you can just put the numbers on there - it is my understanding that the IRS doesn't crosscheck account numbers with taxpayer names and account names.
Theoretically if his assets produced more than $600 in income between his death and the distribution of the assets to his beneficiaries, then you would need to file a 1041 for that income. This sounds unlikely given your descriptions. Even if there were more than $600 earned and even though it is not technically correct, if everyone reports the income they received as reported on the 1099s with their SSNs on it, the IRS will be content and in most cases the resulting tax situation is close enough in my opinion. Life is too short to deal with "interest received as a nominee".
And an estate tax return (706 or 709, can't remember which) would be due 9 months after death if his taxable estate was worth more than $13,990,000. This also sounds unlikely.