So tuns out that the mainboard I have does not want to eat the 4 MB SIMMs.

Likely because they do not have parity chips installed (sigh).

I noticed that the board has a slot for a memory expansion card, which looks like two XT bus connectors back to back (the first one works as an XT bus slot, I checked). Do you know if this connector is standardised and if yes if it's possible to get cards for it?

Missing parity is a likely cause. I'm sorry I didn't mention it when I suggested to get the modules. In typical consumer hardware, parity got optional during the 486 era. Unfortunately, the memory connectors are completely nonstandard. If the first connector is just regular XT connector, the RAM stuff is solely on the second connector. A 386DX system should have 32 data bits, ~10 address bits, 4 CAS lines, one or two RAS lines and a WE line.

Sorry, missing the 4 parity pins, so this is slightly more than 50 connections. Add some Vcc and GND pins, and it still fits the 62 pin XT bus connector. If you are really lucky you can find a matching card by chance on ebay or some local classified ads, but getting another set of SIMMs, this time with parity is likely easier, faster and cheaper.

@fuz They say that RSA with current key lengths (especially above 2048 bits) are computationally very expensive, and they propose ECC as the cure. If you try to authenticate against a RSA4096 server certificate, try connecting to a server using a certificate using the NIST p224 or p256 elliptic curve instead (assuming you compiled bearssl with ECC support).

Make sure the machine uses a cipher suite in the ECDHE-ECDSA family.