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In many cases, the primary power consumer on an Arduino is the power LED. Remove it.

Buck converters are more efficient at high loads, but sometimes have higher standing/quiescent losses. You'll need to select carefully.

At reduced clock speeds, most ATMega parts can operate from 2.7 to 5.5V. Depending on what other parts you have, you may be able to operate directly from a 1S lithium cell with no converter or LDO. You'll still need a battery protection chip/PCB to prevent over discharge.

The other thing you want to do is put the micro to sleep for as long as possible.

Those 5400mWh batteries are a scam. Be very careful with them.

IDK about setting clockspeed in an Arduino, but with a raw atmega328 it's definitely something you'd do. IIRC the atmegas uses fusebits which has to be set during programming. I suspect that you'd at least need to access the ICSP pins instead of programming over USB. At which point you could just build the needed part of the Arduino on perf board and ditch the atmega16u4 and LDO.

If you don't mind 4MHz @ 3V, then the datasheet claims that will draw 1.5mA https://ww1.microchip.com/downloads/en/DeviceDoc/Atmel-7810-Automotive-Microcontrollers-ATmega328P_Datasheet.pdf but if you refer to section 28 in the datasheet you'll see that you can go as low as 2.7V.

If you really have your heart set on the PP3 battery then sure, but I'd probably see if I could use 3xAA instead. I just spent 10s googling, so my research may be lacking. An energizer PP3 lithium ultimate claims 750mAh, if we, for the sake of the argument, don't care about discharge voltage curves and just use the nominal voltage, that makes 6750mWh. Varta has a 2900mAh AA, and 3 of those then become 13050mWh. I know that it's a crude comparison, and you may not get twice the capacity, but still.

If you went for the AAs then your buck will be more efficient as well. Buck converters become less efficient the higher your input voltage https://electronics.stackexchange.com/questions/528284/why-does-converters-efficiency-degrade-with-higher-v-in so you can double the capacity and increase efficiency with AAs.

Like someone else said, pull all the LEDs. There is no point to them if you don't need them. Just because a pin is set low doesn't mean it's completely off, so cut any unused paths to ground to be sure. LEDs still have to reach a specific forward voltage to turn on, but they could still be passing a fractional amount of current.

I believe the internal pull-up resistors are 10k, so if they are enabled, you can disable them and save a few more fractional pennies. (Maybe 3uA per pin if the pullups were enabled to start. Lulz.)

From a software perspective, you just need to keep the MCU in sleep mode as much as possible. Rely on the internal timers to wake up and sleep the MCU and make sure that the main loop is looping as slowly as possible.

That MCU should have an internal oscillator, so test it to see if it saves you any power. Turning it on and disabling the external oscillator should drop the clock speed down to 8mhz and might save you a bit more juice.

Like you said, you can power the 5V rail directly from the buck converter. You can also set the fuses to use the lower frequency internal oscillator. Another good option is that for most of the time, you should keep the atmega in the sleep/low power state, and use an interrupt from a timer to wake the mcu occasionally. You can probably also set up pin change interrupts to wake the mcu as well if say a button is pushed. Additionally, you might be able to disable some of the peripherals if not in use - I haven't looked at AVR microcontrollers in a while so this might not be applicable.

A final option if you really really need it to have low power is to use an external timer ic that turns power on and off to the Arduino. These can have extremely low power draw, and are used on things like door and window sensors to extend their runtime to years by almost eliminating power draw when the mcu isn't running - even the mcu sleep state draws a significant amount of power on large time scales