In HDRP if I have the max amount of punctual lights (2048) performance is very bad, I get about 30 fps. The performance seems to be bad regardless of resolution, or whether I use forward or deferred. Is it possible to run a scene with many point lights in HDRP at a decent framerate, or is this just not possible with HDRP?
Large number of lights will kinda be inevitably very taxing. As usual in gamedev, faking it may be the solution 
Lights are often faked by having a flat, white flare rendered via an additive shader.