No, you do not need to file SSA-1099. Since you are currently receiving SSI from the government on direct deposit, the same information will be used to deposit the Stimulus Check.
From the IRS website
People who aren't typically required to file a tax return
Social Security and Railroad Retirement recipients who are not typically required to file a tax return need to take no action. The IRS will use the information on the Form SSA-1099 and Form RRB-1099 to generate Economic Impact Payments of $1,200 to these individuals even if they did not file tax returns in 2018 or 2019. Recipients will receive these payments as a direct deposit or by paper check, just as they would normally receive their benefits. Social Security Disability Insurance (SSDI) recipients are also part of this group who don't need to take action.
For Social Security, Railroad retirees and SSDI who have qualifying children, they can take an additional step to receive $500 per qualifying child.
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