In simpler terms..
Relatively humidity is a percentage of how close that air is to saturation.
Warm air can hold more water vapour than cold air can, before saturation occurs.

So there can definitely be more water vapour in the air at the equator before the air is saturated - and the air at the poles is so cold that little amounts of water vapour will still bring it relatively close to saturation.

Hopefully that makes sense.
Anyone who reads this feel free to correct me or elaborate.

And for education I found this:

https://www.youtube.com/@introductiontoatmosphericd284

I will need to read more about those things.

I suggest you to sign up to MetEd (https://www.meted.ucar.edu/index.php)
where you'll find a lot of educational resources in meteorological topics.
You can use keywords (e.g. "NWP" for Numerical Weather Prediction)
and skill levels (e.g. "1" stands for easy) to narrow your search.
https://www.meted.ucar.edu/training_detail.php?topicSorting=15&languageSorting=1&module_sorting=skillLevelAsc

Global scale is like the global circulations - like Hadley cell, trade winds, that global transport of heat and moisture to the poles from the equator.
Synoptic Scale is like you see on a weather chart where areas of High Pressure and Low Pressure are identified. Large scale systems, like hurricanes.
Mesoscale is like thunderstorm complexes. Smaller scale things like Tornadoes.
Microscale is like local effects near the ground...like a sea breeze or valley flows type of thing.

and all of that interacts with each other lol

Moisture is even more difficult to understand. When winds blow from North sea to Germany, there is rain. But when winds blow from Mediteranian sea to Egypt, there is no rain, even if Mediteranian sea is more warm then North sea.

@Wheats If I am right, then if temperature drops together with volume, then moisture will not increase. Is here then the answear, why all high pressure areas are dry, no matter of temperature?

High pressure and Low pressure are all about the weight of the atmosphere - how much force is that air putting on the Earth.

Increasing temperature will make air relatively less dense. Increasing moisture will make air relatively less dense. This causes Low Pressure.
Decreasing temperature will make air relatively more dense. Lack of moisture makes air relatively more dense. This causes High Pressure.

High and Low pressure areas will have moisture, whether the weight of the atmosphere will allow the air to rise, cool, and condense is the question and there are too many variables to get into here. The main thing to consider is...in Low Pressure areas you will have air rising from the surface, in High Pressure areas you will have sinking air towards the surface.

You can have Low pressure areas that have hardly any moisture, maybe they are just lower pressure because the temperature increased throughout the day. You can have High pressure areas that have plenty of moisture, but because the weight of the higher pressure air, it will resist vertical motion of the air and have a hard time creating clouds and eventually precipitation.

Like Gkikas-LGPZ said, it's all relative to the surrounding air.

Global circulation cells play a big roll in climate areas on Earth.
You're forgetting about moisture though - lack of moisture is the reason Deserts exist. Technically, Antarctica is a desert. But lack of moisture in subtropical desert areas can be caused by the Hadley cell that circulates warm moist air at the equator northward and southward.

As the warm moist air at the equator rises it expands, cools and condenses - forming clouds and eventually precipitation...This does a few things - causes low pressure, addition of water vapour to an airmass (from the ocean in this case) will actually make the air less dense, along with the increase in temperature, the air becomes more buoyant and rises - this air is destined to rise and rain itself out. As this air moves aloft (northward and southward) it eventually becomes cool enough and dry enough where it sinks towards the Earth's surface and that's essentially where you find your subtropical deserts on continents.

So the Hadley cell moves that warm (because of direct heating) equator air towards the poles.
The Polar cell moves that cold (because of lack of heating) polar air towards the equator.
and the Ferrel Cell is the in-between that helps get it all to where it wants to go.

But this is just an overall look at Global circulation cells - there is a crazy amount going on in the Earth's atmosphere, oceans, and land, and if you are interested in learning more about it I would suggest taking a class or doing some online courses.
These are two resources I used quite a lot before I actually went to school for this madness lol:
https://www.meted.ucar.edu/index.php
http://www.theweatherprediction.com/

Read up and then please, correct me if I'm wrong!

The similar story is in polar cell. Polar cell is also heat engine. But when air reach the ground, all the heat is absorbed by ice.

In Ferrell cell is simillar, only difference is that heat is going to north by ground, not by high troposphere.

If I am not right, please fix me.

Equatorial radius
6378.137 km (3963.191 mi)
Polar radius
6356.752 km (3949.903 mi) https://en.wikipedia.org/wiki/Earth

The centrifugal force even flattens the massive globe, how could oceans and atmosphere not be affected?
It´s just thermo-dynamic embedded in the dynamics of the rotating system.

https://en.wikipedia.org/wiki/Dynamics

The tilt of the Earth and it's orbit around the Sun are what determine where that solar input is most concentrated.

Thermodynamically, that warm air at the equator NEEDS to make it's way to the colder poles.
The Coriolis Force (Earth's rotational force) helps determine the direction that equatorial air moves as it makes it's way to the poles.

The troposphere gets it´s discus-shape mainly through the centrifugal force caused by Earth´s rotation.
If the line of equatorial clouds (= the centre of Intertropical Convergence Zone (ITCZ)) would follow the seasons, it should be expected closer to the locations of Cuba, Emirates, Taiwan in N-summer and Rio de Janero, Madagaskar - Fidschi in N-winter.

So, temperature and height of troposphere is different.

I would better say :
At global scale, the higher the temperature is, the higher is the troposphere.

Polar high:

• high pressure
• low temperature
• low troposphere

Subtropical high:

• high pressure-
• high temperature
• high troposphere

So, temperature and height of troposphere is different.