I believe the first comment already points to some answer, but you had read and pointed at "wrong" part of the Wiki. You should look further below in the Wiki, neatly titled Manually Defined Range of a Page style.

Perform any one of the following commands:

What @Lyrl has explained is the quoted first point in Wiki, "Insert - Manual Break".

[...] I am unable to rotate a page in the middle of the document (in this case, page 98).

It is important to place the cursor at correct position.

First, put the cursor at the end of paragraph in page 97.

Then, do Insert > Manual Break... and choose Page break and Style: Landscape and click OK button. At this point, page 98 and onwards would appear in landscape orientation. So user must limit to which extent the Landscape style would be applied. Continue below.

Next, put the cursor at the end of paragraph in page 98.

Then, do Insert > Manual Break... and choose Page break and Style: Default and click OK. That is all.

Notice the difference when applying the style for the second time? If you follow above steps properly, the landscape orientation is applied to page 98 only.

Try other methods as explained in the Wiki (besides Manual Break, there are three more methods for you to try under this subtopic). Besides these, whatever method you use, take note that the page orientation usually should be handled by page style.

Frankly speaking, Manual Break is the most common and easiest method (at least for me) and it had worked for me regardless I use LibreOffice on Windows or LibreOffice on Linux. There is very slim chances for anyone to make mistake when using Manual Break (It should work for anyone).

I'd think one possible cause it didn't work is that, the existing document might not be using the Default style and using custom/self-defined style instead. This is estimated based on your explanation that "only the first page of document rotates".

If custom/self-defined styles are used, then typical instructions would be invalid. The question has not much clues, so this is as far as I can estimate.