You are correct, you do not pay tax on any on any of that income. You are not even required to file a tax return, unless you need to get a refund on any mistaken withholding.
Your understanding, of the situation, is essentially correct, but not exactly (taxes are complicated and convoluted).
Social security becomes taxable when your income,
including 1/2 your social security, reaches:
Married Filing Jointly(MFJ): $32,000
Single or head of household: $25,000
Married Filing Separately and lived with your spouse at any
time during the tax year: $0
So, half of $30,000 is 15,000. $15,000 + 6500 = 21,500 and that is less than $25,000; so none (0%) of your SS is taxable. So, 0 taxable SS + $6500 taxable pension is less than the $12,000 ($13,300 if over age 64) filing threshold; so you don't need to file.
