OnlyOffice is struggling with the paste operation due to the contents of what you are copying.
What you have is a table cell containing multiple tables, text boxes, and floating images distributed over and around the tables.
I got this far in a few minutes using the documents you supplied.
Which is pretty close to your target I believe.
I just started with a blank presentation page, and then copied from the document to the presentation each of the items, a piece at a time.
First the heading and the cake slice picture.
Then the Ingredients sub-heading.
Then the bottom 3 rows of the table, rows 3, 6, & 5.
Then I inserted a row above and typed in Persons, Butter, etc.
Then I copied and pasted all the pictures.
As each item was pasted into the presentation, they had to be positioned on the page, so for the ingredients table, I left a gap for the pictures above, and then positioned the table and images so they all aligned as illustrated.
The key here is that doing it all in one go, does not appear to work, so piece-meal is the key.
I think it was the table and images of the ingredients was the key problematic issue. The Vocabulary table copied in one go without any issue, as with the bottom rows of the ingredients.
A bit of jostling of the elements should get it to fit the slide page.
If you don’t mind, I will join this thread.
I’ve tried to copy\paste the data as you described in the original scenario into the new slide (Add slide) in your pptx file and I faced an issue. Please confirm that this is your usage scenario, so we can start our checks.