What do I do if I've deleted as much as I can and still don't have enuf space to install Big Sur

You will need to move/delete more. Get an external hard drive and put your space hogging things on it (videos, music, photos, etc), then delete on the internal drive.

You need a minimum 35 GB of space for the download/install; if coming from an earlier/older OS, then it's up to 45 GB space needed.

And, you do realize that you need to always maintain an absolute minimum of 10 - 15 GB of empty space?

The "storage" is much more than that - it is where your OS and all of your files are and the OS needs room to function properly. If you fill up your disk, your computer will stop functioning - it is that simple. It will be very difficult to try to get files off at that point.

You need around 35GB free before downloading the installer (some 23GB if the installer has already been downloaded.

I can understand it is hard when the system drive is a paltry 128GB. How big is your iMac drive and how much free space do you have?

You can try restarting in Safe Mode, which clears a number of system caches, which may sometimes grow quite a bit, but you should know that some free space is always needed for the OS, even when it is not being upgraded. A full disk causes severe performance issues and potentially fatal crashes.

but I don't have any apps on my imac. Why is that?

Where are your apps?

Regardless, that storage display is not only the size of all the apps. It includes data generated by the apps.

All photos are on the cloud as are most of my big files. Sigh!

Which cloud? iCloud synchronizes files to your Mac. You can store them only in iCloud, but unless you specifically did that, there are copies on your Mac.

Check your Applications folder - there should be apps as they are installed be default and are part of the OS install. And, if they came with the OS, you should not and cannot delete them. Including the third party apps I've installed, my Applications folder has about 36 GB. My entire Macintosh HD has about 180 GB taken up out of a 500 GB SSD.

So, nowadays with the OS taking up more and more space, 128 GB is really very small. And, as mentioned, your photos are still on your hard drive - note: if you delete them, they will disappear from the icloud. Put them on an external drive.

If I offload photos and then delete them from my HD won't they also get deleted from the cloud?

Depending on where they are located, then yes. But deleting from the cloud is not your issue. It's the other way around. Just because it is stored in iCloud doesn't mean it is not also stored on your drive.