It may depend on which Pi2 revision you have. If it's rev 1.2 then (according to Wikipedia) it has a 900MHz 64-bit quad-core ARM Cortex-A53 processor which is the same as the Pi3B (used in the stock DGTPi) but running slower (1.2 GHz in the Pi3b). So, in this case, you might be able to run the v3.3
64-bit Bookworm Lite image (modified for stand-alone operation). Otherwise, if it's a Cortex-A7, you will have to use a 32-bit OS and may have some success with the 32-bit v3.2 Bullseye Lite image. Note that the Bullseye image has not been updated since the last release. See
this thread for links to the Bullseye images. I would not recommend a Desktop image. Perhaps someone who owns a Pi2 can provide their experiences.
Randy