Okay, it took some time, but I managed to crunch the numbers by census tract. This doesn't give us neighborhood-level granularity everywhere. I believe that all Pittsburgh neighborhoods were based upon census tracts back in 2000, but the Census has been merging low-population tracts for some time, meaning I can't crunch the numbers of the smaller neighborhoods. on the other hand, some of the bigger neighborhoods can be given added granularity here. It looks like the actual boundaries changed a bit (beyond mergers) in Lincoln-Lemington-Belmar and the South Side Slopes, so those numbers may be off.
For every tract, I listed the numeric gain/loss. The map also uses blue and red to signify percentage gains and losses, with darker shades of red meaning deeper losses, and darker shades of blue bigger gains. Colors are in 5% increments.
Going round the city:
Central: Simply massive growth in Downtown and the Strip District. Surprisingly there was some growth in parts of the Hill District, but this was canceled out by losses elsewhere. Oakland's gains were more mediocre than I had expected, which may have to do with the pandemic and less students being in housing. Uptown had a big decline, which is probably due to variance in the population of the County Jail.
Upper East End: Notable nodes of growth in Lower/Central Lawrenceville, East Liberty, Bakery Square area, and parts of Bloomfield (by the new apartment building. Garfield came very close to growing, which really surprised me. The Greater Homewood area continued to hemorrhage population however, other than Homewood South, where the new construction came very close to ending the decline.
Lower East End: Overall modest growth here. The large growth in a portion of North of Forbes surprised me. This is the area around Chatham's campus, and may have to do with student housing. The most student-slummy portion of Squirrel Hill shrunk a bit, but the rest grew. Greenfield as a whole came very close to growing. Hazelwood is still declining significantly.
South Pittsburgh: As expected, little to no growth outside of South Side Flats, but the rate of decline was lower than I expected. Carrick actually gained population - I have to wonder if the Nepalese refugees played a role, as the tract with significant growth is now the most Asian part of Carrick (8.7%).
West End: Shockingly, the Greater West End grew over the last decade - albeit only by 7 people. It's hard to say where this growth was with the data I have, because so many neighborhoods are merged by the Census in the West End.
North Side: Very disappointing numbers overall, even taking out of consideration the massive decline caused by the closure of SCI prison. It looks like the additional inhabited apartment in Allegheny Center did cause significant growth - and unlike what I said last night, Central North Side did grow a bit. But almost everywhere else in the North Side experienced steep declines. I'm not sure what's going on in the tract which includes Northview Heights and Summer Hill. There was a new mini-development in Summer Hill this decade, but I thought it only had maybe two dozen houses. I suppose more people are living in Northview Heights? Most of the North Side seems to have declined at a rate between 5% and 10% for the decade, with Fineview declining more (due to the paring down of Allegheny Dwellings) and Brighton Heights and Marshall Shadeland (excepting the prison) declining by less.]