What is this bottom bracket standard called
The bolt in the cranks means you have a 3-piece crank (separate left and right crank arms and cartridge bottom bracket, with a square taper or splined axle-crank interface).

No power meters come in this type of crank because it's old technology that only appears on inexpensive bikes these days. 

However 3-piece cranks use a threaded bottom bracket shell, you can replace the bottom bracket with an external bearing one and fit modern 2-piece power meter cranks (axle is permanently joined to drive side crank). There are a few standards: Shimano HollowTech II, SRAM GXP, FSA MegaExo. To reduce cost you could find a lightly used crank on Ebay and a compatible left hand side crank arm power meter.  

Another path to go is power meter pedals, which will not require replacing the crank and BB at all of course.

BTW, you don't need a power meter to track improvement. A smartphone or bike computer and Strava is a great tool for that. Power meters are expensive,  given that you likely have a bike on the older or less expensive side you might be better off using the money on some bike upgrades.