When I use migration assistant to restore a backup from my time capsule onto my new iMac, will the backups include settings of 3rd party apps like 1Password, Dropbox etc, or does it only save core mac preferences only.
Yes, settings of 3rd party apps are included.
Time Machine does not do a full backup of your computer but it it designed to backup up everything you add to the computer in terms of apps, settings, and pretty much everything from your Desktop picture to your spellcheck settings in Microsoft Word as well as all files and folders you make.
You can list items to ignore as can developers for files that are temporary, working data, cached data that can be recreated again.
You are able to disable certain folders from being backed up, so if any third party preferences are contained in one of those folders you will not be able to retrieve them.