Replacing CMOS SRAM with equivalent TTL SRAM
You're confusing the manufacturing process of the AS7C4098A (which is CMOS) with it's compatibility (which is TTL and CMOS). Compatibility here refers to I/O levels and means that the AS7C4098A will connect to and work with other parts that use either TTL or CMOS logic thresholds.

This is all about reading and understanding the DC characteristics section of the datasheets, comparing the Voh/Vol and Vih/Vil parameters of the devices you are connecting together. And I'm not sure you've understood the absolute maximum ratings section - the 7V you quote is an absolute maximum supply voltage above which you will damage the SRAM, so what do you mean when you say this is "adequate"?

Make sure your STM32 (which is presumably powered from 3.3V) is going to be OK working with a 5V powered SRAM, i.e. that its inputs are 5V tolerant.