I have an Arduino Nano clone with an external gyroscope and SD-card writer connected to the 3v3 pin. When I connect the Arduino with a cable to my laptop everything works fine.
After that worked I tried powering the Nano with a single coin cell and a step-up converter to 5v. The Vout connected to Vin on the Arduino. This did not work.
Then i tried the same connection, but with two coin cells in series and a step-up to 9v. This worked for a few seconds, after which the voltage dropped below 5V on the Vout of the step-up and the writing to the SD-card stopped working.
The last thing I tried were three coin cells in series with the 9v step-up. This did not improve anything.
Q1: Is there any way to make this work for a longer time (I need it to be able to work for about 6 hours)?
Q2: Would it be a possibility that this setup would be suitable with the Arduino Nano 33 BLE since it has a lower Vin input voltage?
Q3: I need to use a flat battery since the idea is to make a wearable data logger. Do you know of any battery options that would be better suitable?
Two coin cells in series will give 3V which is OK for your setup.
Your Nano consumes a lot of unneeded power (LED, USB, voltage regulator); a 3.3V / 8MHz Pro Mini might be a better choice, especially if you remove the LED and the voltage regulator. SD cards are 3.3V devices and your gyroscope probably as well.
You will have to test if your components will work on 3V with two coin cells; you will also measure the current that is used to be able to predict how long your battery will last.
Q2
With built-in BLE, it will probably consume more.
Using an Arduino usually cost plenty of power. SD cards are notorious for their power consumption, especially during writes.
If you wanna use a coin cell battery, build an Arduino from scratch. Exclude everything DC - DC conversion since it converts precious power into heat. An ATMega or ATTiny MCU can run just fine from 3 V. Implement sleep states into your code, and if possible shut down sensors that's otherwise just idling.
Right, my wife just reminded me: Welcome to the Arduino forum!
Most Arduinos are not intended for low power operation, so coin cells are out of the question. A 2xAA battery pack will work fine for years, if you make some modifications to the board and use sleep modes or power down intervals.