I think Puerto Rico has a stronger case for statehood than DC. The National Mall, White House, Capitol, and federally-owned office buildings would remain under direct federal control under pretty much any proposal, so I'll ignore those and talk about "DC" as if those sections had already been excised from the discussion.
Democrats see DC & PR statehood as a big boost to efforts to gain (technically "retain") control of the Senate and White House. (DC has a lot of federal workers and Black residents, both of which have skewed Democratic for the past couple decades.) I prefer not to be overly bluntly political: Cynical power-seeking alienates people I'd rather convince, and sets bad precedent for self-serving policies. (One case is Republicans’ bluntly political move to admit sparsely-populated Western states, which is now being cited as precedent for the admission of DC.) That means we need to justify policies and federal decisions in ways that resonate outside the narrow group of people who stand to get immediate, obvious political gains. At some points, states have been added in pairs to roughly split the Senate between the parties according to the politics of the time. (See especially slavery.) Expect Republicans to argue that because the Constitution (Article I Section 8) says Congress has to exert direct control over the "seat of government", that must include the entirety of DC and its population.
How would you justify DC / PR statehood to a conservative, Republican resident of Montana? What does it mean to be a state and how is it important outside the Senate and Electoral College? Why make DC & PR their own states instead of leaving them as they are, or merging them into neighboring states? Notably, while Puerto Rico’s residents are roughly evenly split on becoming a state, DC favors statehood by a significant margin.
I think the "taxation without representation" argument has some merit here, but not as much as DC-statehood-proponents usually assume: We could get representation for DC by merging it into MD (or VA, but the Potomac already makes an obvious natural border.) DC has a population of roughly 712k, more than either Wyoming or Vermont. There are 19 US cities with more residents, so if DC is its own state, why not Houston, Denver, Los Angeles, or Seattle? (There are 6 territories according to Wikipedia's list above, but the smallest four together have a population less than the smallest state.)
Also note that Puerto Rico has a population of 3.2 million, making it the largest US territory, and instead of being bigger than 2 states, it's bigger than 20. I'm not sure how PR's politics goes these days; my understanding is the two major parties' politics get shifted a bit there. That might make it a less-reliable Democratic vote, or a Democratic one on some issues and Republican on others. _If_ it's politically flexible, you might have an easier time getting it past objections that statehood is just self-serving politics for the party which is currently in power.
Moreover, if states are supposed to be methods for local autonomy, ways for people to customize laws to local climate, politics, priorities, and culture, DC is very similar to Northern VA and suburban MD. Again, you could satisfy that requirement by merging the residential portions of DC into MD - or making the DC state include everything inside the Capitol Beltway and/or served by the DC Metro bus & rail system. There are some cultural features that are also strongly associated with DC (Go-Go music, working in the federal government), but I expect those don't have hard boundaries that happen to coincide with the District's borders. I expect you just get back to the metropolitan area as a cultural block... and that you could make similar arguments for other large cities being their own cultural units / states. Again, though, Puerto Rico's geographic isolation gives it a strong argument for statehood under this thinking.
So there you have my point of view: Short-term, DC shouldn't be a state, but should be merged into MD. Puerto Rico should be a state, because it passes a couple of conceptual thresholds that DC does not. This might not be enticing to the Democratic party, but I think it's going to be resilient at avoiding charges of self-serving politics and thus avoid "slippery-slope" arguments, cynicism, and no-holds-barred political payback.
Long-term, the country should have a discussion about what it means to be a State, and how that concept has changed since the country's founding: The population has become much more mobile, and long-distance communication, travel, and commerce are much more important than they used to be. Politics have accordingly become more nationalized, state borders less important, and the urban/rural divide more pronounced. More people are living in cities; fewer are focused on agriculture. Are those changes important to how the Constitution is interpreted? What standards should we have for adding new states? Under what conditions should we merge existing states or push them back to "territory" status? The resolutions emerging from that discussion should be written into the Constitution as Amendments.