DDMunday, Horton Iris Gardens and C & T Iris Patch both carry Immortality. I have ordered from both of them and always receive excellent quality rhizomes, most of which bloom the next season after I plant them. (Planting in late summer to early fall, they usually bloom the following spring for me in Zone 5, southwest Kansas.)
Another option might be Shreiner's Iris Gardens. Their prices are usually higher but they also usually send larger, more developed rhizomes that are even more likely to bloom the following spring.
Added on 12/17/22: I just remembered... In 2021 I ordered three rhizomes of Sugar Blues from Shreiner's. Sugar Blues is a rebloomer. All three of those rhizomes produced bloom stalks that same year. I planted them in late July or early August and they bloomed in late September or early October.
If you ordered Immortality from Shreiner's in 2023, there's a decent chance you might see blooms in fall of 2023. No guarantees but certainly possible.