Under normal circumstances it takes the IRS 16 weeks to process an amended return (Form 1040-X). But circumstances are not normal this year. The IRS is extremely backlogged, so it will take many months for your federal amended return to be processed. No one can give you even a rough estimate.
I don't think the states are in as bad shape as the IRS, but each state processes its own tax returns, so they're all different. You might get your additional state refund before the federal.
