Yes... Well.... as is so often true, what is "simple" for the cognoscenti is less than clear for the rest of us... So, having muddled through this (with many disconcerting crashes of Calc along the way), I will offer the following details, which I hope will be helpful:
1) To create a an appropriate Style, select:
Format > Styles > Styles and Formatting . This will open a side panel entitled "Styles and Formatting".
(oops... ha-ha... In actually going through the steps for purposes of this post, Calc crashed YET AGAIN

: as it has done maybe a dozen times in trying to figure out how to do this. The "Document Recovery" procedure generally works, as it did again this time... but it's been frustrating. And just in case it's relevant to anyone, when Calc restarted, I was in a different side panel, for "Styles" rather than "Styles and Formatting"....
So.... Let's see... Where was I? Oh, yes... )
2) In the <Styles and Formatting> side panel, there are icons in the upper left corner for two tabs: "Cell Styles" and "Page Styles" (based on their ToolTips popups).
Select <Page Styles>.
3) Assuming you've not already defined any new styles, only two predefined styles will (might?) be present: "Default" and "Report". To create a new style, right-click anywhere within the side panel, and select "New..."
4) A dialog window will open having 7 tabs.
In the "
Organizer" tab, enter a name for your new Style. In separate steps, I created TWO (2) new styles, called "Landscape_Layout" and "Portrait Layout".
5) Then, in the same window, select the "
Page" tab, and indicate the desired page orientation using the radio buttons.
Then, click "OK".
6) Your new style(s) have now been created, but are NOT YET associated with the active worksheet. To accomplish this:
a) Make sure the desired worksheet is active (Selected). Then,
b) in the Styles and Formatting window, left-click-and-HOLD the corresponding style ("Portrait_Layout" or "Landscape_Layout", in my case) UNTIL the name becomes highlighted in gray. (er.... that's "grey" for many of you). You can then select another worksheet and attach a different style.
There are evidently many more formatting features you can set in "Styles"... but what I just wrote represents 100% of what I know about it, or
intend to know.
I've become so unhinged

by the notion of "Styles", after having (
painfully) struggled and suffered with them for many years in Microsoft Word, that I would
never have clicked on the Format-Styles in Calc, if this apparently were not the
only way to get different sheets in the same workbook to print at different page orientations.
Hope this helps.