A fuse and an MCB will not do any harm - leave the fuse in place if that's easier. I have an MCB in my own control box - first thing the mains gets to, before anything else, so that virtually everything in the box is then "downstream" of the MCB. Didn't help when I refitted something and put a bolt straight through the insulation of the incoming mains cable without noticing - tripped the ring main MCB (32A) plus consumer unit RCCD (60A, I think). Didn't blow the 13A fuse in the control box mains plug, or the one in the extension lead plug. That might tell you something about MCB versus fuse performance!

Don't care if the motors take 10A, say (if the PSU could deliver it). That's at a low voltage. The problem here is that the incoming mains is at a much higher voltage. For the same power, the higher the voltage the lower the current - power = volts x amps, in simple terms. So if you take 10A at 36V from the PSU, that's 360W (watts). At 240V, that's 1.5A (=360/240). I'm simplifying slightly here but that's pretty much correct.

Don't care about driver ratings, big or small. It's what they actually deliver to the motors that matters; Stepper drivers usually have a "max current" adjustment, so a "big" driver could be set to 2A while a "small" driver could be set to 4A, perhaps; Daft way round to configure them, but it's possible. If they both use 36V, then the power delivered (which comes from the PSU) will be 36x4 = 144W or 36 x 2 = 72W. So, forgetting any power loss in the PSU (which will be small) then this is the power taken from the mains. But that is delivered at 240V. Current draw of 144W at 240V = 144/240 = 0.6A or so (I'm doing the sums in my head).

To calculate the MCB size needed you have to estimate the current going through it; start with the power that the load takes (volts x amps). then convert this into current at 240V (power / 240). You are limited by whatever your PSU is rated at - 350W, it says, and whatever you try to draw from it, the PSU will limit to this value - so at mains volts that's 350//240 = 1.5A (near enough). You can connect to 100 stepper drivers of whatever rating you like - but that PSU will still limit you to a total of 350W (7.3A at 36V, like the ad says) in any case.