Installing a slot drain afterwards, any experiences?

Hi hi dear community,
I once started a thread titled " ". I have made my decision and I am looking forward to the work.......................

But to largely avoid something like this, I would like to retroactively install a slot drain. Since the water always stands on the left side and does not drain away.
In the picture, you can see where I would like to build it (marked in red). The red circle shows a connection point to the infiltration trench.
I would place a maintenance shaft in the middle.

Would you take on the work?
What disadvantages would I have later with such a drain? Are there any experiences here?

The water is on the left, as seen from the photos? On the "trash bin side"? Along the entire length? Or just at the corner? If it's along the length, you have to plan the channel rotated by 90 degrees. Anyway, if the channel should have the slope the other way than the terrace, it will be a deep channel towards the right... Or am I just understanding everything wrong? :D

Is the water standing on the left, as seen from the photos? On the "trash can side"? Along the entire length? Or only at the corner? If it's lengthwise, you have to plan the channel rotated by 90 degrees. In general, if the channel is supposed to have the slope opposite to the terrace, it will be a deep channel to the right... Or am I just understanding everything wrong? :D

The water stands on the left when viewed from the front in rows 1 and 2. The slabs have also been laid quite level there and the water does not drain away. You can also see where the water stands by looking at the green areas.

The slabs have also been laid quite level there and the water does not drain off.

Isn't that the actual problem? Or is the water standing so heavily on the grass that it then runs onto the terrace? In that case, as a cheap solution, I would dig out a spade width, replace a bit of the subsoil with coarse gravel, and possibly sand the topsoil a bit. That should allow for significantly better infiltration.

Okay. But in what way does the gutter then help the water drain on the horizontal plates? And as I said: If the water is standing lengthwise on the left side, you also need a gutter on the left side, lengthwise. You would need a gutter with an integrated slope there.

Isn't that the real problem? Or is the water standing so heavily on the grass that it then flows onto the terrace? In that case, as an inexpensive solution, I would dig out a spade's width, replace some subsoil with coarse gravel, and maybe add some sand to the topsoil. Then it should infiltrate significantly better

So we have laid a drainage pipe along the curb stone. Gravel etc. was all taken into account. The water stands well there. That the slabs there are level will be the little problem. However, it is a lot of water coming from the garage. I just want to say… that I am currently paying a good tuition fee and learning from mistakes☺️