i think qgis might have the ability to do everything you require, however the learning curve is somewhat steep.

it allows you to import data from various maps, including openstreetmap, NASA and many more.

i believe there are free/open source topographic layers that can be imported or ways to add specific data.

it can draw layers, lines and shapes on top of each other with varying translucency and colors.

it can show non-mercator map projections such as stereographic, othrographic or even more obscure ones like the waterman butterfly or some of the ones from the list at the bottom of this page: http://www.quadibloc.com/maps/mapint.htm

if you are doing this for a fantasy world map and not earth, it might add even more difficulty but i've read people on forums claim they could do it, using another program with qgis and on windows only. i don't recall much else since the windows requirement was a block for me. it's probably possible to create the shapefile from scratch.

it has the ability to customize aspects of maps and mapped datum in many more ways that i am incapable of properly explaining, describing, using or understanding. i also have cognitive/developmental disorders, so it might be easier for others, however for me, it's a map creation program i get lost trying to use.

OpenStreetMap and their editors are great and I use them a lot, but if you really want to have great flexibility with your map design QGIS is Open Source

Here's a video on how to use it

https://wiki.openstreetmap.org/wiki/Editors#Choice_of_editors

Something like these?

You can check out the toolkit over at Permapeople.org, though I'm unsure exactly how open the codebase is. I do know they're hoping to make it community run in the future, and that the devs share pretty much whatever is asked of them.

Less in the spirit of your question, but something I've used relatively extensively is the mymaps.google tool. Here's hoping someone with some better answers than me comes along (and I remember to check back) to give additional alternatives

Would https://umap.openstreetmap.fr/en/ work for you? It's Osm plus markers etc(?) you can put on top of it. Not sure if you can make it work offline/selfhosted. I used it for marking interesting locations in a city some friends wanted to visit that I know quite well.