yovish

As for programming PROM memory, I leave that to be answered by those creating new routines for programmers.

However, testing some memories can be problematic because Logic Tests can only contain 512 lines, and this does not allow you to test 1024 memory cells. It is also impossible to test most of the memories that have 512 or 256 cells, because the test consists of writing some value and then reading it (2 lines). There are always a few lines to check various additional logic states of such memory.
Additionally, the Logical Tests interface does not help in creating long writes. Maybe one day this interface will be improved, but for now, it's troublesome.
For testing such memories, the T56 and TL866II programmers are not suitable for now...

yovish

Despite what was written earlier, it is possible to create some Logic Tests. If you have SRAMs that you would like to check very often, then you can write Logic Tests yourself.
It will be time consuming and a little complicated, but it may be worth it. I, for my own purposes, use the TL866II programmer for various tests. If I need the Test to have more than 512 lines, I make several smaller ones and test each one in turn.
Almost every electronics engineer is able to write even simple tests, and then you can already try more complicated ones...