Magento 2.3.5 migration - Category IDs not correctly set in corresponding tables. (Fix related to error 404 / Knockout bindings not working)

[ChameleonDevil]

Preconditions

1. Magento 2.3.5 clean installation
2. Magento Data Migration tool v2.3.5 with config for source data Magento 1 : 1.7.0.2

Steps to reproduce

1. Setup clean installation of Magento 2.3.5
2. Migrate Data but make sure to rename Magento 2.3.5 attribute set names (otherwise this tool complains and fails with DUPLICATE IDs)
3. After renaming existing M2 attribute set names migrate M1 data.
   bin/magento migrate:data path/to/config.xml

Expected result

1. A working Magento 2 setup with migrated data.

Actual result

Besides other issues also failing (not related to this discussion), the category's are not editable in the backend, category data is not bound (only default data shown), frontend category landing pages also not working (missing)!

Issue

Data migration tool does not import and fill database tables correctly when 'Default' attribute set is also in source database. Only partially fills database correctly.

Database tables catalog_category_entity and eav_entity_attribute are involved with this issue.

Solution - Database side

The full question and solution (from database side) is on my topic here:
Magento Stack Exchange solution

It would be great if this can be applied on the data-migration-tool directly.

(I have to do alot of things over and over when reimporting, including this).

[ChameleonDevil]

I potentially think this issue also fixes the 404 category errors after migration as well. Please confirm if anyone else are having same issue.

[p810]

We're noticing an issue today where none of our migrated categories have names. Do you know if this could be related to the problem you were experiencing? edit: Or, have you encountered this problem yourself?

[ChameleonDevil]

Do you mean in the database or just in the backend? This issue relates to bindings not working (and then showing empty values in the backend) but the data is still intact in the database (well most of the category data), and the solution is which I added on Stack Exchange. You update the migrated data to the correct attribute set id. If it helps you please vote there :)

For instance this query confirms your values:
SELECT * FROM catalog_category_entity cce INNER JOIN catalog_category_entity_varchar evar ON cce.entity_id = evar.entity_id WHERE evar.attribute_id IN (SELECT attribute_id FROM eav_attribute where attribute_code IN ('Name') AND entity_type_id = 3)

Note: entity_type_id = 3 on my instance.
Also, other category attributes are also in the text, int, etc tables like catalog_category_entity_varchar.