Well, too many things to explain, I hope I don't go on too long and make everything understandable.
Don't worry about blank spaces
First of all, don't worry about blank spaces, rather worry about poor distribution. According to the explanation, it's a very technical website, whose content depends on data. If this data is not enough to occupy the entire graphic area of the page, instead of fighting to eliminate the resulting empty spaces, the solution is to find a way to make these spaces as balanced as possible.
This is the structural scheme on page 1:
This is the structural scheme on page 2:
In the two images, it is clearly seen that the blank spaces are totally unbalanced: margins, gutters, distances, etc. How to solve it:
Use a structural design
The problem with most web designers is they think of graphic elements above the structural axes on which they are supported. It's like designing a car from the lights, doors, and windshield without thinking about the car body. The title, the buttons, the text, the menu, the dropdowns, the tables, etc, all of these are compositive elements. It's very important to establish a support where to place them. If this support is well structured, no white space will be out of place:
If the design is well structured, the empty "hole" will become part of the design instead of being seen as an error or absence.
- Take the objects to place as something secondary (at least in
this first step)
- Find repetitive matching distances
- Try to make equal partitions: 1/2, 1/3, 1/4, etc.
- Constantly look for central axes, mainly vertical.
There are several graphic resources to solve the wide empty spaces, it depends on the design and the objective. I only cite one example of those who have been able to take great advantage of blanks and from which several ideas can be drawn: Swiss editorial design
There are more empty space problems on this page than in the two images in the question:
However, the balance is given by a clear structuring, the compensation of visual weights, and some graphic resource, such as the lines that delimit the composition areas, even though these later do not carry any element.