Anyone can make a mistake when publishing an ad when selecting the category and they should be able to modify it, because otherwise the person is obliged to delete the ad and republish it, which I think is nonsense.

Yes, I mentioned reasons about, but in your case with 1 big category this issue looks more uncomfortable than usual situations.

Is there an approximate date for the launch of the "Jobs" module?

I guess it will be released with UNA 14 stable.

I understand that you mean not using the categories used by the "Ads" module and adding my own category field.

Yes, in your case with 1 main category (Jobs) it's better to have own subcategories.

I think I would lose the classification of the ads by categories/subcategories that the module offers.

You may try to use this variant for subcategories to keep main features:

https://unacms.com/wiki/Browseable-categories