Following the end of the New Kingdom (c. 1110 BCE), Egypt entered into a long period of decline. During this time, the authority of the central government often broke down. For example, during the 21st Dynasty (c. 1069 BCE - 945 BCE) the country was effectively divided between the pharaoh in the north and the high priest of Amun in the south. For the next several centuries, there were period of unification followed by period of disunity.
Egypt also had to contend with the machinations of foreign powers. Egypt's southern neighbors, the Kushites conquered Egypt around 712 BCE and ruled for approximately 100 years (though they were careful to rule as traditional pharaohs). They were subsequently pushed out by the Assyrians in 671 BCE, who turned Egypt into a vassal state. Although the Egyptians eventually threw off Assyrian control, they promptly had to contend with the Babylonians and then the Persians. The Persians would go on to conquer Egypt twice (first, from 525 - 404 BCE and then from 343 - 332 BC).
The Persians were in turn expelled by Alexander the Great. Following Alexander's death, control of Egypt passed to one of his generals, Ptolemy, and Ptolemy's descendants would rule Egypt until the country was annexed by Rome under Augustus in 30 BCE. Although the Ptolemies and the Romans were careful to preserve the fiction that they were traditional pharaohs, they generally kept native Egyptians away from political power. Both the Ptolemies and the Romans favored Greek speakers for administrative positions.
Despite all this political chaos, Egyptian culture remained strong. Some of the most magnificent temples in Egypt (e.g., the temple of Edfu) were built during the Greco-Roman period, and there remained a lively Egyptian literary tradition. The traditional practice of mummification continued (it was even adopted by some Greeks and Romans resident in Egypt), and new religious texts were composed (e.g., the Book of Breathings, which is essentially a later version of the Book of the Dead). Some Egyptian deities (e.g., Isis and Serapis) became popular throughout the Roman world. But with the advent of Christianity in the fourth century CE, traditional Egyptian culture began to wither as the pagan temples (which had preserved their culture for so long) were closed.
The TL;DR of it all is that Egypt suffered considerable political instability during the first millennium BCE, which led to foreign conquest. However, a distinctly Egyptian culture continued until well into the Roman period.
Here are some books you might check out if you'd like to learn more about the end of Egyptian civilization:
The Twilight of Ancient Egypt by Karol Mysliwiec
The Third Intermediate Period by Kenneth Kitchen
Egypt After the Pharaohs by Alan K. Bowman
The Oxford Handbook of Roman Egypt by Christina Riggs
Religion in Roman Egypt: Assimilation and Resistance by David Frankfurter
Related question: When did Egypt stop being, "rich"? It used to be the breadbasket of the Mediterranean and it was a critical loss for the Eastern Romans in the 7th century. Was it still a breadbasket through the Ottoman Era, or did it decline during that time period?
As you pointed out yourself, they simply just changed in different ways
Other people can probably answer your quesrions better but I'll try and link relevant threads
/u/bentresh talks about changes within ancient egypt (doesn't really fit your question but you'll probably find it interesting nonetheless
He also talks about the change from hierogylphics to demotic and coptic egyptian