How do I know that my text messages have been saved on my iCloud?

go to Settings > [your name] > iCloud.. is the switch turned on for Messages? If it is ON, then your messages are not included in your iPhone backup, they are stored in iCloud. If the switch is turned OFF, then your messages are included as part of your iPhone backup.

Backup methods for iPhone, iPad, and iPod touch - Apple Support

If not using message in iCloud, to know that they are included?

Well I suppose you'd have to erase and restore your iPhone from that backup just to see.. which doesn't make a whole lot of sense. Unfortunately you can't really sift thru the data contained in an iPhone backup.

Now that.......may be a real problem. Last time I checked, there was no PC version of Messages.

I don't have a PC here at this time to verify though, so maybe one of the other PC guys can answer on that one.

Did you check the position of the switch I inquired about? (Settings > [your name] > iCloud > Messages) Is it ON or OFF?

I'm assuming ON if you expected to see messages when logging into iCloud?

The lack of messages icon when logging into iCloud should not be of concern. You can't use iCloud.com to view your messages, regardless of the position of that switch.. regardless of the type of computer you have.

If the switch is ON, then your messages will not be included in an iPhone backup as they are synced in iCloud instead. If you had another Apple device using the same Apple ID (such as an iPad or a Mac), you could turn on messages in iCloud and start seeing your synced messages populate on that device. Without another device, you'll more or less just have to trust that they are there.

If you go to Settings > [your name] > iCloud, you can see the breakdown of your iCloud storage. If you have enough messages, it'll start to represent a chunk of space in the bar graph.

You don't need to do an iPhone backup to sync your messages, they sync as you get the messages.

If your phone ever takes a dump, you'd restore your iPhone from your latest backup, this should include positioning the messages switch correctly, and your messages would start loading from the cloud, just like all your apps etc.

I use messages in iCloud. I upgrade my phone every year. I still have messages from 5+ years ago.

You did set up Messages on your Mac, correct? And, work through the options, correct?

Set up Messages on Mac - Apple Support