No. The IRS doesn't update Turbo Tax. But if you log back into your Turbo Tax Account it may update and show the new refund. But they might have stopped doing that.
There's no way to track the IRS. Just keep waiting. The IRS is sending them out in batches over the summer.
See IRS article May 14, 2021
https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-...
And see,
https://www.irs.gov/newsroom/irs-sending-more-than-2-point-8-million-refunds-to-those-who-already-pa...
