The next step is to implement LoRaWAN on the Pi. The RFM95W handles LoRa but does not include a LoRaWAN stack. TTN requires LoRaWAN (and not much else).
Yes, most of the LoRaWAN implementations are either on an accompanying MCU, or a connected Arduino. LoRaWAN on Pi implementations are less common, but there are a couple.
Start by checking out the efforts to including LoRa in the kernel. This email will provide good context, particularly this section:
Ready-made LoRa hardware modules come in three flavors,
a) with SPI access to the underlying Semtech chip sets, needing a software implementation of e.g. LoRaWAN protocol stack (i.e., a soft MAC),
b) with a custom, often UART based interface and a pre-certified LoRaWAN
protocol stack already integrated (i.e., hard/full MAC), and
c) with a microcontroller that serves not only for the protocol stack but
also as application processor, not offering a ready-made interface.
Then check out the lmic_pi project. LMIC is a popular LoRaWAN stack for Arduino and Ernst de Vreede has kindly published their efforts to port it to Pi. It happens to have been tested with the radio you have in mind.