Nothing baffling about it - modern crypto is a lot more resource hungry than those of twenty years ago.
What you can and should do, is reduce the number of simultaneous https connections to a minimum, so you don’t end up performing a denial of service attack against yourself
There’s no good solution to crypto on classic Amiga hardware, other than offloading to other processor, dedicated crypto accelerator or general purpose modern CPU (that often have crypto accelerator built in), but then you must find a way to interface such hardware to the Amiga.
