POSTGIS now supports outputting vector tiles as endpoint to a Query. https://postgis.net/docs/ST_AsMVT.html I honestly don't recommend this approach because currently that's just geometry and no attributes.
You can also pair POSTGIS with GeoServer and GeoWebCache to produce vector tiles but also don't recommend that.
But probably your best bet now is that GDAL 2.3 supports Writting Vector Tiles both in Folder of XYZ PBF and inside sqlite3 container mbtiles. https://www.gdal.org/drv_pg.html
OGR2OGR can read from your POSTGIS database and write an mbtiles. It's slower than Tippecanoe and has less options. So you may also want to use MapBox Tippecanoe which is also free and open source. Tippecanoe can be run on Windows SubSystem for Linux (WSL) Bash Ubuntu (as well as Linux and Mac operating systems). It will require the data to be in GeoJSON (and CSV is supported) file to convert to vector tiles. Tippecanoe also has GeoJSON extensions for Zoom Level and Layer Name so you can have super granular control over the production of vector tiles. For polygons use the -pD option to not show tile boundaries and for most of the time don't do buffers.
One last point is that you can use ESRI ArcGIS Pro to create vector tiles so you can connect your POSTGIS database. You need to create a Vector Tile Package VTPK and then convert that to mbtiles or extract to folder.