Me and my friend are designing a USB powered F4T5 programmed start ballast, if anyone could provide me with the filament heating voltage for one that would be great!
to answer the direct question asked, for an ANSI specification 4W T5 the cathode heating voltage is nominally about 8V, you can read more about the exact details and allowable ranges/tolerances in the C78.81 standard for fluorescent tubes
https://www.nema.org/docs/default-source/about-us-document-library/ansi-c78.81-2016-(r2022)_aspublished.pdfbut are you looking to design a program start that preheats the cathodes for a fixed amount of time and then fires the tube or a continuously heated cathode rapid start ballast?
different design criteria exist with regards to cathode heating voltage/currents so the distinction is fairly important
for a program start ballast you will want to implement a fixed constant-current based preheating method rather than a fixed constant voltage method