The issue you are seeing is that Fusion 8 will not run on Monterey. VMware had to make changes to Fusion to run on Big Sur and later due to Apple changes to macOS. These Apple changes mean that the older Fusion release is incompatible with Monterey..

There's nothing you can do other than install Fusion 13 to run on Monterey. Before doing that, you'll need to:

Drag the Fusion 8 application to the trash from your Applications folder. You may also want to see if you have any other files lying around by referencing the information in the article https://kb.vmware.com/s/article/1017838. - even though it's for Fusion 10 and later, there might be some help to identify some of the "hidden" support files that Fusion places on your disk.

You will need to purchase a new Fusion 13 license (see if Fusion 13 Player will work for you as that's less expensive that Fusion 13 Pro). Your Fusion 8 license won't work for Fusion 13, there's no upgrade pricing for Fusion 13 from Fusion 8, and if you're using it for your business you aren't eligible for the free Fusion 13 personal use license (IMO).

Once you've done these, then download Fusion 13 from VMware and install it. 

Your existing VM won't be touched by this process, although you may need to open the VM manually the first time. 

You should also immediately re-evaluate your backup strategy. Time Machine is not a recommended method of backing up virtual machines. Vmware talks about this in the Fusion documentation.  Time Machine is terribly wasteful of backup storage when used to try and back up virtual machines. More importantly, Time Machine backups of VMs frequently results in corrupt VM backups. You won't know that the backup is bad until you try to use it and find out that it's corrupt. You should consider backing up files from within your VM like you would a physical machine, or shut down the VM and use the Finder to drag a copy of it to another non-Time Machine external drive. 

(or investigate a VM-specific backup utility such as Vimalin (www.vimalin.com).)

Thank you Paul for the incredibly detailed reply. I very much appreciate you taking the time to share your knowledge.

Understood on F8 will not work on Monterey. I had a look at the VMWare website and from their table showing the differences between Player and Pro, the features of Pro seem to be things I will not have much use for. We are mainly a Mac house and use Windows solely for QuickBooksPro2015. And since our needs in the accounting sphere are very modest, I am hoping to continue using QBP15 for as long as possible.

I hear you on the Time Machine question. The main reason the previous iMac had a Time Machine backup was because it was getting long in the tooth and I started to be concerned about potential hard drive failure. I created the Time Machine drive to serve as a backup for when we migrated to the new machine. I will read up on the information from VMWare and look at other solutions, including Vimalin.

Thanks again!