The behavior was changed to make it more robust and more standard conformant.
I don't have Excel at hand here but when I try in online Excel in OneDrive, it fails by default and puts everything in a single column, but there is a "Paste options" button with a "Split Text to Columns" option where I can select the correct variant. (edit: I can also do this after the paste by selecting the cells and doing Data > Split Text to Columns).
Are you saying that the version without the quotes is splitting the columns by default correctly on your machine and the one with the quotes is not?
The quotes should really not change anything. They are necessary if the text can contain the decimal separator which is the case here since the headers are user-entered text.
When I paste in LibreOffice, if I keep the headers, it automatically shows the text import dialog. Then the values are imported as text or as numbers based on the decimal separator.
If I paste in Google Sheets it's the same as OneDrive Excel, fails by default but there is a button "paste formatting" with a "Split text to columns" option with the options.
"Time (ms)";"Trajectory 1"
"133";"142.0046"
"167";"150.0579"
"Time (ms)";"Trajectory 1"
"133";"142,0046"
"167";"150,0579"
Time (ms);Trajectory 1
133;142.0046
167;150.0579
Time (ms);Trajectory 1
133;142,0046
167;150,0579