Another way that the original/freeware version can be played is with the use of a newer engine, such as NXEngine or CSE2. The one I would recommend is a version of CSE2 called "Cave Story: Tweaked". It adds many accessibility features in addition to a great deal of other nice upgrades, such as widescreen and better fullscreen support. The CSE2 repo and all of the forks were taken off Github due to Nicalis filing a DMCA takedown request, which means that the main page for downloading the source code and the release packages isn't available. However, the last release version of Tweaked can be found on the Doukutsu Club page located here:
https://doukutsuclub.knack.com/database#search-database/mod-details/5ecc783fee5fa10016eef82e/
You should be able to just download one of the .zip files, extract it, and run the game without any additional setup. If it sounds good to you, give it a try and see if that works better.
Also, please stop spamming links to your Discord server