iphone is broken and wont plug in, icloud not backed up due to low storage, how can get data from broken phone

So it won't connect at all? I'll just say that I had an iPad Mini 2 that had a completely trashed screen assembly + home button and I could back it up by connecting it to a computer. It would respond to the alarm from Find My iPhone and I could get statistics on it including battery charge level from a computer. So you don't even have that?

Honestly the only way would be to have it repaired enough that data can be recovered. If there's anything wrong internally, Apple won't do it. The only option Apple usually gives is a complete replacement and absolutely no means of recovering the data. They consider the proper backup of data to be the user's responsibility.

Of course nobody here knows enough about the condition or why yours no longer works. There are services that might be able to recover the data, but they're all outside of Apple's repair ecosystem, where that ecosystem is mostly limited to replacement of batteries/screen assemblies or complete exchange of the device with a replacement device.

Do you have an idea of why it's broken? Water damage. Screen broken? Dropped hard? I can't and won't give you any recommendations, but there are services might have a policy that they can recover data or there's no charge. Typical data recovery services include a repair that gets the data off the device, but not a complete working device that should work indefinitely. This kind of service is expensive, may cost more than a new, equivalent device, and (if successful) doesn't include a long-term working device.

Sorry, but no.