Based on my experience on releasing a secure IoT device on a microcontroller: You will need to spend a lot of time optimizing that. The most used TLS library (mbedTls) requires 20kB send and receive buffers for each connection. That doesn't involve buffers for the TCP/IP stack yet, and also not anything for an application. You can reduce the buffer sizes, but then you are no longer standard compliant (at least on the receiving side) and if the server sends longer TLS frames the device might close the connection or exhibit undefined behavior.

You can either experiment with other TLS libraries or investigate whether a more powerful device wouldn't make your life easier.