A solution

Ok, lets face it. David Decker is a single person and he does not provide a solution for the problem that after updating Elementor Pro to 3.10 and above the templates kind of not work anymore.
I hope he (David) is well.

The only solution is to deactivate this plugin and live without it.
There are three things to consider:
1. The Dynamic Tag
2. Language Menu
3. Synchonization of templates between languages

Lets begin with 3. Synchonization of templates between languages:
As far as I know the only way to get around the problem is to have only one template for all languages. And we are talking only about the templates of Elementor, e.g. Template Builder.
For example: on our site (spl.audio) we had a Header and a Footer template, each in german and english. After deactivating the plugin the german templates were shown in both languages, the english templates were not used anymore (this can be different on your site, you have to check which language template is shown after deactivating the plugin).
So I copied all the english content from the english templates into the german templates. Then I used a plugin to dynamically switched the visibility of the german/english contents based on the language.
You can do this with the plugin Dynamic Conditions By RTO GmbH which is free. I use Crocoblock JetEngine which has a Dynamic Visibility feature.

1. The Dynamic Tag
To show or hide sections or widgets depending on a language with a dynamic condition plugin you need a so called Elementor Dynamic Tag for the polylang language. The Polylang Connector plugin provided a dynamic tag for the polylang language. But as we deactivated it we need our own dynamic tag. I made a simple small plugin which provides this Dynamic Tag.
It can be downloaded here: https://next.spl.audio/index.php/s/NCXZjDTs2jdf9ty
Please note: This code ist just an example to write your own code. Do not use this code directly. I can not give any support.
You also may have a look how David Decker did the dynamic tag in his plugin in the folder modules.

2. Language Menu
For the language menu you need to code your own widget. This is not so difficult. Get inspired by the code from David Decker. Again you find the widget code in his plugin inside the modules folder.

Thats it.