When will e-filed for amended returns be available through turbotax?

Sorry--no one knows that yet.  It will probably be months away.  Even the IRS has not announced when except for sometime this year.... And when they do begin to accept e-filed amended returns it will require a lot of new programming for tax software, which takes time.

https://www.irs.gov/newsroom/irs-announces-form-1040-x-electronic-filing-options-coming-this-summer-major-milestone-reached-for-electronic-returns

you can't e-File amended returns without tax software.

Therefore, obviously, the tax software must be ready by sometime in late summer.