Is Touch ID compatible with older iMac 27

No it is not possible, you need a M1 or later based iMac to get TouchID. It may be time to upgrade to a new computer anyway.

A lot of folks that are upgrading from older iMacs are getting the new M4 based Mac mini and an external display. You can get a MM with 1TB of SSD storage for $999 add $300 for a nice display and you may need a couple of USB to USB C adapter (<$10) and for less than you paid for your iMac 13 years ago you have a computer that FAR outperforms you old machine. You can use the old Mac's mouse, buy the TouchID keyboard with the MM and then recycle the old iMac for free using one of Apple's recycling programs ( Apple Recycling Programs ).

When the new machine arrives just use the steps in Setup Assistant and Migration Assistant and you are done!

Good luck.

An iPad might be a better choice than a Mac.

That’ll get you either Touch ID or Face ID, and has a simpler and far more portable touch-based user interface.

Whether an iPad as replacement will work though, depends on which apps you need.

No, the facility that allowed for that Target Display Mode has been deprecated for years

Use your iMac as a display with target display mode - Apple Support

There are software solutions, such as AirPlay, but they may or may not work for you.

And if you don't like typing on an iPad you can use an Apple BT keyboard with the iPad. Also there's a case with keyboard for the iPad if you want to take it on the road.