When Joomla is installed all modules have the tag div and the header is an h3.

The landmark issue can be solved by setting a different module tag.
Open the module and go to tab Advanced.
At the option Module Tag change div to something else, the usual options may be nav, aside, section, but you have more options. It depends on what you are displaying and where...

Under the same tab, at option Header Tag you can set the tag for the module title.
Depending on the order (of modules) and/or selected tag, changing this may solve the invalid heading order.

In the case of the change in the module that you described, the problem in axe disappeared. What about such elements that are not in the module and as I understand them are elements of the Cassiopeia template or others, e.g. the enabled accessibility add-on, there are several issues. The following issues are not in the module, so I guess only the change in the template code and the Accessibility plugin and js files in the media/vendor/accessibility/js location? But what exactly needs to be changed? I list them below

Ensure all page content is contained by landmarks
[more information https://dequeuniversity.com/rules/axe/4.10/region?application=AxeFirefox

#back-top

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
[more information https://dequeuniversity.com/rules/axe/4.10/region?application=AxeFirefox

._access-icon

♿

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
[more information https://dequeuniversity.com/rules/axe/4.10/region?application=AxeFirefox
Element Location:

._text-center

XAccessibility♲

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
https://dequeuniversity.com/rules/axe/4.10/region?application=AxeFirefox

li[data-access-action="increaseText"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information https://dequeuniversity.com/rules/axe/4.10/region?application=AxeFirefox
Element Location:

li[data-access-action="decreaseText"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="increaseTextSpacing"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="decreaseTextSpacing"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="invertColors"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="underlineLinks"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="bigCursor"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

li[data-access-action="textToSpeech"]

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

the accessibility plugin is useless and should not be used.

it does NOT make anything accessible

For what purpose is it distributed with the Joomla system and other similar plugins with other competing CMS systems? I know that in reality usually disabled people have different other readers depending on the disability. This can often be confusing to the average person.

it was first included at the request of the joomla accessibility team as a tool that some people might find useful.

IT is not an accessibility overlay that claims to make anything accessible.

IT is supposed to be a tool that might improve the use of a site for some people with accessibility needs that do not already have their own accessibility tools such as a screen reader. (for example the site has been badly designed with small fonts so the occasional user might find it useful to use the tool to increase the font size - something that they have never needed to do on other sites so they do not know how to do it in their browser). How useful it is will be subjective and site specific. Thats one of the reasons it is NOT enabled by default.

Unfortunately for many the plugin itself creates its own problems assuming that you are relying on automated tests to tell you if something is accessible or not

After disabling this Accessibility add-on, there is only one issue left, which is shown in Axe dev tools. How to solve this. It's not in any module but in the Cassiopeia template code?

Ensure all page content is contained by landmarks
more information Link opens in a new window
Element Location:

#back-top

To solve this problem, you need to fix the following:

Some page content is not contained by landmarks

that is an option in the template style

I know that when it is turned off it does not show any accessibility error but sometimes a button to the top of the page is useful when there is a longer page and it scrolls to the bottom you can quickly return with the button to the top. Is there anything I can change in the code so that the error does not occur?

When AXE finds an issue, it does not mean your site is not accessible, nor does it mean your site is accessible when AXE finds no issues.

AXE is a helpful, but automated, test.

Your website is built for humans, not AXE.
To be sure about accessibility, a human test is needed.

Browse the page only using your keyboard.
Can you tab through the page?
Can you read/hear the content?
Can you see/hear if you can reach the back-to-top button?
Is it in a logical place?
Are you able to use the button?

I understand, I just use tools Firefox Axe and https://wave.webaim.org that help in working on eliminating accessibility errors. Yes, I have the TAB key enabled to navigate the page and I have the menu enabled. Skip to navigation plugin
https://forum.joomla.org/viewtopic.php?t=994294
The text was listened to audio when the accessibility module was enabled. I currently do not have an audio reader because this add-on is disabled. I disabled the back to top button because it causes issues which I described above.