if there’s a change in interest rate, will that affect only the asset side, or affect both asset side and liability side?
Change in interest rates would affect assets and liabilities. However you immunized your portfolio so the surplus is affected by the change of interest rates.
Your assets that were used to immunize your liabilities net out if you were immunized - so the change in interest rates would affect the balance of assets used to immunize your liabilities - this doesn’t eat into the surplus. Your surplus is like an asset only portfolio so the interest effects will play a role in how it moves up or down- the assets used to immunize the liabilities will move together.