OsmAnd does not use the OpenStreetMap standard tile layer (also known as openstreetmap-carto) to generate its maps, so bugs related to maps rendered for OsmAnd do not belong there. OsmAnd uses its own tile render generation routines, generally defined in the OsmAnd-resources GitHub project.
{"api": "MBTiles Server 3.3.4","http": {"GET": ["/<mbtiles>","/<mbtiles>/{zoom}/{x}/{y}","/<mbtiles>/WMTS","/<mbtiles>/WMTS/1.0.0/WMTSCapabilities.xml"]},"mbtiles": ["mt"],"ok": true,"protocol": "http","cache": "/home/user/mbtiles","port": 5000,"status": 200}
{"version": "1.1.0","type": "overlay","minzoom": 6,"maxzoom": 15,"description": "Montana Private Parcels and Public Land","name": "Montana Private Parcels and Public Land","bounds": [-116.04914578697117,44.357921825347965,-104.0396585815126,49.001105491109875],"center": [-110.044402,46.679514],"format": "png"}

Does that mean my attempts were doomed from the start? :-)
I don't think so! If you're serving tiles in a format like:
https://servername/directory/0/1/2.png
then you should be able to set it up.
I have a server https://map.atownsend.org.uk/ that serves tiles in the usual OSM format, so https://map.atownsend.org.uk/hot/9/253/166.png is a valid tile. I've defined that in Osmand via "Map Source / Define/Edit" as:
Best Regards,
Andy
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