The old tiny2313 could read fuse and lockbits but not Signature/Calibration bytes.
When the tiny4313 came out, RSIG is shown in the "24. Register Summary" in the shared "ATtiny2313A/4313" data sheet.
The "19.7.1 SPMCSR "“ Store Program Memory Control and Status Register" paragraph also shows RSIG.
It does not always appear in header files!
Anyway, when I ordered my STM32F429 Diiscovery kit, I added a couple of tiny2313A chips.
I tried using RSIG bit to read the Signature/Calibration with the same program that works for tiny4313. And RSIG does not exist.
Of course, the 2313A also is supposed to have USIBR register and USART_MSPI functionality.
And the 2313A has the same Signature as the 2313.