Does the prayer of the Imam and the congregant become invalid if the Imam recites the end of a short surah after Al-Fatiha while raising his hands for the takbir to bow, instead of completing its recitation and then performing the takbir?

Reciting something from the Surah after raising the hands for Rukūʿ does not invalidate the prayer. It is recommended for the Imam to pause between the recitation and the Takbīr for Rukūʿ with a slight silence, to allow him to catch his breath. The number of silences for the Imam and their recommendation is a matter of disagreement, as some scholars believe the Imam should have two silences, while others believe he should have three.

And Allah knows best.