Same here.
Using the Energizer Ultimate Lithium since 3 month.
They‘re Not rechargeable and u will Not find Lithium batteries with high runtime as rechargeable.
And Trust me, u Need Lithium batteries, if u doesnt want to have Problems with your doorbell.
On my g410 doorbell, I use EBL rechargeable 1.5v batteries and have had success. I was having the same rapid depletion issue with normal 1.2v rechargeable batteries. I am one month into the EBL 1.5v and the battery meter hasn’t moved at all.