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The "mixing up of the html-table" could have various reasons, e.g.
related to CSS.
You can compare the HTML/CSS code that you have to, this example and see if there are any differences:
https://tcpdf.org/examples/example_048/FYI: I copied your table and pasted it in publisher on my PC, but without your CSS, and the PDF was created correctly:
I have the same version of TCPDF: 6.2.13