1. You can go for Silent key switches, or install o rings and or landing pads on a standard mech board/kepcaps. These do reduce noise, but the switches are still louder than typing on membranes because they don't address the return clack of each key. Topre boards are quiet - they're like posh rubber dome/membrane boards, but they are expensive.
2. Then just buy another rubber dome and live with it?
3. The layout with the undersized entry key is ANSI.
Cheap backlit TKL but ISO not ANSI
This one is ANSI but with a "mechanical feel" - its also waterproof so it likely has a membrane, which usually means quieter operation.
Failing that - Aliexpress is loaded with backlit tenkeyless boards, but you'll have to sift through them to find non-menchanical boards.