Can I erase Data but not apps before giving away my iMac?

IdrisSeabright is correct. The apps from the Apple App Store will remain associated with your Apple ID, and cannot be updated without your Apple ID credentials. Third-party apps can be similarly tied. So… no. This won’t work.

If you are part of a Family Sharing group with the scions, many App Store apps can be shared.

For the reset… Download macOS Catalina, build a bootable installer (links to the Catalina download), and use that to factory reset the Mac.

Not having the bootable installer handy means booting from Recovery (use option-Command-R), and that boot can sometimes be dicy on older Macs.

You can remove the data but may or may not be able to keep the apps. However, DO NOT erase either Macintosh HD or Macintosh HD Data, as that would end up corrupting the whole system; you would have a heap of trouble trying to recover.

Regarding your user data ...

Assuming you have only 1 user account on your iMac, it is an Admin account and you should never remove that account; it's the primary account by which the Mac is managed.

• Just remove all your user data that's in your home folder; and/or in other folders you may have created on the drive. But don't remove any of the top-level folders in your home folder, just their contents. The top level folders are Desktop, Documents, Downloads, Movies, Music, Pictures and Public.
• Then change the password for that account.
• Then create a new User Account (System Preferences > Users & Groups) for your grandkids to use. You can make it an Admin account if you want to.
• It would also be a good idea to create a second Admin account to protect against the risk of your first admin account ever going bad. It would not actually be used unless necessary.

Regarding the apps ...

You need to check the licenses for each to see if you are allowed to transfer them to another owner/user. Not all licenses allow that. If not allowed you would need to remove those apps.

All in all, it would be preferable to erase the drive & reinstall macOS from scratch, treating the iMac as a new machine 'owned' by your grandkids, using their AppleID and licenses for other apps.

You would need to erase the drive and reload any software you had permission to include. Not all software licenses allow you to pass the software on to someone else. Those that do generally require that you include any and all disks and delete the applications off all the devices you're keeping.