and if you're running a version of PostGIS with protobuffers enabled (Not AWS RDS) you can generate vector tiles on the fly with https://postgis.net/docs/ST_AsMVT.html
which are great for displaying large datasets.
v10.5 of postgres by the looks of it, don't know how I missed that.
You'll need the MapboxVectorTiles plugin for leaflet but you can definitely improve the sizes by a fair bit.
I've done this for GeoJSON tiles for a long time, before the MVT tiles. The MVT tiles pack way more data though, but are not a solution to the O(n2) problem.
Also, as others have mentioned you can generate the st_asmvt format directly from pg. This plus PostgREST binary output can get you a way to query your table directly through a REST API.
It looks like the city of Chicago might be sitting on top of the Socrata API, which allows you to run a distinct - if you are visualizing counts for each tract (or averages and other types of calculations) it would save you the Digital Ocean resources to grab the API counts either on-the-fly or as static files for the tracts in Chicago and render them that way via Leaflet, but obviously this does not allow for quite as novel an analysis as PostGIS offers! (here's the API page that the City of Chicago links to from their page https://dev.socrata.com/docs/functions/#2.1,)
One of my favorite primers is by Robert Simmon who I had the pleasure of seeing at OpenVis: https://youtu.be/N_dmiQI1s24
RE mapping tools - I've been working a lot lately with Vector Tiles and their embedded props and from a web-mapping perspective it's nice to download the geometry once and then style many times in terms of over-the-wire efficiency.
Happy hunting and thanks for your post.