My hesitation arises because my external hard drive is not with me, so I am unable to perform a back-up.
It is wise to hesitate. You simply must not make any system upgrade (not even an update ) without making a full backup of your computer. it is extremely risky. Even if nothing goes wrong during the upgrade you will not be able to revert to the previous system, if you should notice major problems after the upgrade, like incompatible applications, device drivers, or data formats. If you only can get to High Sierra, you may not be able to upgrade all applications to High Sierra compatible versions. The AppStore has moved on to Mojave and Catalina versions.
I can indeed view my photos in iCloud and on my newer machine. Now that I recall, I think I have had My Photo Stream on since December 2019. I just turned it off to see if the photos will remain in iCloud and Photos (2015 mach) after 30 days.
The photos you are seeing in Photos on www.icloud.com are safely stored in your iCloud Photos Library.
ut there may be many gaps, if you only transferred photos using My Photo Stream. My Photo Stream is only ta temporary buffer. It is transferring recently added photos to iCloud - a different section from iCloud Photos - and other devices need to have My Photo Stream enabled to download download them during the month the photos are there and import them.
There are many possible complications making this setup messy, if you mix it with iCloud Photos:
- The videos are not transferred. Live Photos will be turned into still frames.
- The adjustments are not transferred - only the originals.
- You may have duplicates in several sizes, if you have been using My Photos Stream on Macs and iPhones, iPads, iPods. The problem is, that each device is downloading and saving My Photo Stream items in a size optimised for the device. When you enable iCloud Photos you may be seeing the smaller My Photo Stream versions from the iPhone or iPad in addition to the original high resolution version. You may also be seeing duplicates of edited versions and originals, broken Live Photos.
I would not rely on the My Photo Stream transfer. Once you upgrade to the newest version your system can manage, you can convert the iPhoto Library to a Photos Library and let iCloud merge the libraries properly. Photos 3 on GG´High Sierra is the first version that can sync named faces with iCloud.