You’re correct, only use the new ST app. I’ve updated the post to reflect that change and also the link on how to exclude devices using the new ST app.
As for what are device handlers, read this short blog which explains the various components of SmartThings and the purpose of device handlers (TLDR: they allow SmartThings to communicate with devices). There are some built device handlers like Z-Wave Lock for the Kwikset lock which allow basic control and ability to program it and then there are custom lock device handlers which allow you to access your locks advanced features, improve the stability/reliability of the lock etc.
When a lock doesn’t pair correctly, the hub doesn’t know which device handler to assign the lock (this happens due to radio interference which impedes the communication while pairing and thus prevents the hub from correctly identifying the lock leading it to be assigned a generic Thing designation). The solution is the post above or manually assigning the lock the correct device handler.