Rauno's CNC router

[JAZZCNC]

Therefore a rigid design is a must for the machine in order to make nice looking aluminum parts.

If your main goal is to cut aluminum then you need a stronger base and gantry along with a ridged Z-axis.

Mainly considering this due the lower price of 1605 ball screws.

It would be a mistake to go for RM1605 for a machine this size, I wouldn't even use 1605 on a smaller router because you still need a certain amount of speed to cut materials like wood and MDF correctly, and using 1605 means your motors are always spinning fast when cutting at higher feeds so torque is low and often very near the stall point.
RM1610 gives you all the speed you require while allowing the motor to spin slower with higher torque while cutting. Careful not to get caught up in the resolution trap either because you don't actually need high resolution for the type of materials you are looking to cut and a 10mm pitch with micro-stepping drives will give you more than enough resolution for most types of cutting.

I plan to order water cutting of the parts.

Careful with water jet cutting because unless it's cut very slowly you will get a tapered edge.

Gantry beam: 4080 aluminum profile with sheet metal reinforcement. I know the 45x90 design recommendation, but it would cost me 60€ more, yet I am open to your opinion - is the 45x90 L design gantry worth this money?

I've built literally 100's of machines now using the 45x90 with my "L" design gantry so I'm probably a little biased, but it just works and pound for pound it's the strongest arrangement I've ever used. Yes, I've built and still do build machines with stronger gantry's but they are much much more expensive and complicated to build and can only be done if you have a CNC machine to start with.

Do I need that expensive motor+driver for Z axis?

Yes, don't underestimate the Z-axis, it's THE most important part of the machine, if the Z-axis is weak or underpowered it doesn't matter how good the rest of the machine. Also, if you plan on doing 3D type work or V-carving which has lots of Z-axis movement then you will need plenty of power with a reasonably heavy spindle like a 2.2Kw.

If I understand correctly the toroidal transformer could power those VAC capable Lichuan drivers directly with AC current. One thing to consider is the input grid voltage, as my place has solar panels and this could cause bigger voltage fluctuations than the grid itself has.

We fit 55Vac transformers on the machines we build using these Lichuan drives and with a 230V - 55Vac transformer on a UK grid which runs around 240Vac the output usually runs around 60Vac so I would expect you'll be ok because I think your grid will be more like 220/230Vac and the Lichuan drives will handle 70Vac and I know from experience because of a transformer sizing error that they will take 72Vac without damage.