What was "high" from 2015-19 is not the same in 2023. $160 mil/yr isn't even median payroll.
You are right. In terms of CBT, 15th is ChiSox at $194 million CBT, 16th is StL at $193.9 million. In terms of 26 man payroll on Opening Day, that 15th was StL at $176.5 million, and 16th was Colorado at $172.1 million.
https://legacy.baseballprospectus.com/compensation/cots/What I take from that is that as long as the Nats have most of their positions from 2025-29 filled by pre-arb and low cost controlled guys, they can assemble a pretty competitive roster with 2 or 3 high priced FAs without even coming up to a median payroll. A line up with just 3 hits among the position players (could be House / Crews / Wood, but you could slot in Lipscomb, Morales, Vaquero, or even a lesser guy), plus Abrams and Ruiz, doesn't have a ton of weak spots you need to splurge on. Soto easily fits in there. Rotation might be more of an issue, but a lead dog pitcher to go with Gore and a couple of hits among Cavalli, Sykora, Gray, Irvin, Rutledge etc.. gets you pretty close.
As for how do you pay for it? Well, I'm assuming that all this stuff about the Nats actually being a team that doesn't qualify for revenue sharing and that ranks them as a top market has some basis, even with the messed up MASN deal. Until you start seeing this team in the bottom half of estimated market value, it's reasonable to assume that smarter people than us have a basis for saying that.
That said, can any team afford 2 or 3 albatross contracts plus pay for the 3 or more good FAs to play key roles? I think even the big money coastal teams would have trouble. Braves and Dodgers have had the skill and smarts and luck to avoid the albatrosses, but I don't think the same can be said of the NYY and BOS. As for the BJs, Philly and Mets, jury is out.