This is a very interesting question, and the linked study does not address it, only "net migration" to "other parts of the country." IANAD[1] but I suspect the census estimate data is not actually capable of addressing your specific question - how could you tell who was coming from where? But as jeffbee suggested there might be a way to tease it out.

The study mentions remote work being part of the reason for the shift; this also confounds "city-to-suburb" versus "city-to-Midwest" migration since it's harder to cross-check against employment statistics - again, without more detailed surveys.

[1] Demographer :)

The census does and it's accessible https://data.census.gov/table/ACSDP1Y2022.DP05?q=population

If you click the drop down where it says "DP05: ACS Demographic and Housing Estimates" you can select which year's estimate you want to use (or use the Decennial Census). If you want a specific geographical area, click Geos.

Then you can get data at whatever level you'd like.

Well, here's some anecdata:

I'd been living in NJ for a few years before the pandemic and,just before the pandemic, had finally saved up enough for a down payment. We started looking summer of 2019, and were picky and not in a rush so were still looking when the pandemic hit. What this meant is I got to do a compare/contrast on my town's housing market. Right after everything shut down, there was no activity for a few weeks, but by spring things were restarting (with masking, or even virtual showings). What I saw is that inventory didn't increase -- maybe even decreased actually, as people weren't eager to move -- but demand became insane as people fled the city. Houses went for $50k or more over asking regularly -- the same houses we'd looked at the summer before and passed on because of shoddy construction or suspiciously strategically placed drywall in the basement.

I actually kept a spreadsheet to help me figure out how much we'd have to bid to have a chance without over bidding. We were finally successful in 2021, so got to take advantage of the super low rates, even though we ended up paying more up front.

Here's the summary stats I ended up with, sale dates 2020-06-25 through 2022-03-18

    Square Feet Listing Price Sale Price List vs Sale List vs sale % diff
  Mean 1,993.36 $568,002.74 $615,661.54 $52,770.80  9.67%
  Median 1,872.50 $550,000.00 $610,000.00 $51,900.00  9.60%. 
  Max 3,700.00 $1,399,900.00 $1,400,000.00 $225,000.00  37.28%
  Min 1,140.00 $300,000.00 $285,500.00 ($127,000.00) -19.54%
  Quartile 25% 1,607.25 $495,000.00 $527,750.00 $14,750.00  2.78%
  Quartile 50% 1,872.50 $550,000.00 $610,000.00 $51,900.00  9.60%
  Quartile 75% 2,300.00 $625,000.00 $690,499.50 $91,250.00  16.72%

The CSA population declined 2.6% from the 2020 decennial census to the 2022 ACS. Note that these are not directly comparable surveys.

If you click into the article, they have it broken down by boroughs.