Is it understood from Al-Kasani's words that speech before the Takbir does not invalidate the intention, and is this ruling applicable in the four schools of thought?

The Hanafi jurists have determined that a separation between the intention (niyyah) and the takbir does not invalidate the prayer if it is not due to something extraneous to the prayer. However, if it is due to something extraneous to the prayer, such as speaking about worldly matters, it does invalidate it. What is meant by "extraneous" is anything that is not fitting for prayer, such as eating, drinking, and speaking. As for walking and performing ablution, these are not considered extraneous.