I need help with choosing battery for my project. I have an arduino nano 33 iot and need a battery that is compact and easy to charge or change
The Nano 33 IOT does not have a battery input, so you will also need a boost converter if you use just one Li-ion battery.
If you use two in series you can connect them to Vin
I would use two 18650 batteries.
the 18650 Battery Shield V8 Mobile Power Bank has 5V and 3.3V outputs and can be charged from a USB port
how long the battery support last depends on the load - you can try putting the target micro into sleep
Post a proposed schematic showing what you want to put together. Also note the current each module requires. Then determine how long it has to run on batteries.