The building isn’t rated as a residence, so it’s most likely a fire code violation to use it as a residence. Aside from that:

squatters benefit from free utilities, cable TV and internet access, and cleaning services. This may violate congressional ethics rules, which prohibit members from using official resources for anything other than incidental personal needs. At the least, lodging on government premises should be treated as a taxable fringe benefit – in the same way that congressional parking spaces are.

https://www.bloomberg.com/opinion/articles/2018-04-06/u-s-lawmakers-shouldn-t-be-sleeping-in-their-offices

So, while there isn’t a rule that says specifically “congresspeople may not sleep in their offices”, there are all kinds of rules about what constitutes housing in DC that are not met by congressional offices:

https://dob.dc.gov/service/dc-housing-code-standards

https://realestateinthedistrict.com/is-your-dc-bedroom-legal/

How about Arlington or Alexandria?

That’s still going to be a second residence, it may not be a $2500/month residence, but it’s not going to be free.