Voltage from batteries in series operating on 3 ATTiny, 3 Buttons, and 3 Piezo buzzers
If you connect the AtTiny chips in parallel, they will all receive the full voltage from your battery. If you exceed the current output of your battery the voltage will droop.
If the AtTiny chips need 3.5V and you give them 6V instead, it will likely destroy the chips.
The short answer: Don't try to drive microcontrollers directly from batteries. You should get a 3.5V switching power supply. Then you will be able to drive all 3 chips cleanly from your battery. (Switching power supplies are very efficient. They don't waste much power at all.)
Note that button cells produce very small total power (in milliwatt/hours) so they won't drive your processors for very long before they are exhausted. I suggest using 4 AA batteries and a switching regulator instead. The 4 AA batteries would give you a 6V VIN to your voltage regulator, but a lot more total power.