How to control the number of measures per line of music

There is no setting that will do exactly what you want. The default is for MuseScore to fit the measures on a line based upon spacing of the various measure elements number of notes in the measures, much like what you are asking for. If there are consistently too many lines for you, then you will want to add line breaks from the breaks and spacers palette. If there are too few measures you may consider changing the Scaling in the Layout->Page settings... menu. There are other settings in the Style->General... menu that affect page layout as well, but there is no reset to default. If you don't like the results you will need to remember the settings. These settings are mostly easily understood, but you may need to refer to https://musescore.org/en/handbook/layout-and-formatting#style-menu in the handbook.

If you need a bunch of four measure lines, consider the line break tool:
https://musescore.org/en/handbook/tools#line-breaks
where you can break lines every 4 measures (and then manually adjust if you need a line with five measures).

Regards.

The short answer is, add line breaks, just as you would when writing poetry. Whether you do so from the Breaks & Spacers palette or using Edit / Tools / Add/Remove Line Breaks, either way the result is the same - MsueScore is smart enough to know you want the second thing you pictured, not the first. That is, it knows music is normally spread out to fill the width of the page; it doesn't need to be told that. It's possible to force MuseScore not to fill a line to the page width, but it's extra work - you need to add a horizontal spacer after the last measure and add the break to that.

I think one ought to keep in mind that poetry always has an optical element. The shape of the lines and strophes on the paper is part of the overall impression you get from a poem.

Not so in music. Unlike for poems only performers usually read music. Very few people can read (and hear in their heads) more than simple melodies--and most can't even read and hear those. But everybody can read poetry if they make the effort. So musical notation is strictly practical (although it can look beautiful if done nicely); the effort is to make it easy for the performers to read their parts / scores.

To push measures to the next line, use the line break tool, as already stated. But to do the opposite in a simple manner that is easily reversed, try the following procedure:

A simple way to get more measures into a line that sometimes quickly makes the adjustment, like when you just want to keep one or two measures up in the previous line, is to select the entire line along with the measures in the following line that you want to keep all together in one line. Then "decrease stretch" using the Layout menu/Decrease Stretch. Keep applying this to the selection until it fits or until Musescore can't do anymore. The effectiveness depends on how many notes and such that the music contains. This is a simple fix for situations that really just need some nudging, without needing to meddle with other layout parameters.

You can add system breaks in MuseScore v4.
This can be done in Format / Add/remove system breaks / Break systems every n measures.