Live in Seoul and used ICN in February and have used it regularly for the past seven years.
Delta check in, gates and all operations are in T2. You can not access it from T1 check in area.
Garuda check in is at T1, but a quick check of Flight Aware shows they use the 111/113 gates which are the Concourse.
So you will land at T2, follow transit signs. You will take the train to the Concourse gates. Presumably you will have to visit a transit desk to get your Garuda boarding pass along the way.
They should check bags through.
if not, you have to clear immigration at T2. Then take the shuttle bus approximately 20 minutes to T1, check in at Garuda counters. Can also take a train, but by the time you walk down to the station etc it’s going to be the same as the shuttle on the road.
Then check in at Garuda T1. Once you pass security there, take the train to Concourse gates.
The Concourse gates are bare. If you can, visit the lounges/restaurants etc at T2 before taking the train to Concourse.
You cannot move between T2/Concourse/T1 freely. You have to scan boarding pass to move fully in one direction at a gate before the train.