Selfhosted

If it's strictly for personal use, Nextcloud can do this easily (no upload required since the client handles the sync), although it's a very heavyweight way to do it and for security reasons most people probably have Nextcloud set up behind a VPN-wall like Tailscale or something so it may not work for you.

However, it technically has a share link feature that does exactly this. If you're using the desktop or mobile client you just have to put it in one of Nextcloud's sync folders and then right click on it or whatever to get a share link to the file. You can also do it through the web UI (both the upload itself and getting the link to it) You can make the share link public and permanent so anyone who can access the Nextcloud server can get access to that file through the link.

Worth considering if you already have a Nextcloud instance. Alternately, if you aren't already using Nextcloud for sensitive personal files, and just want a repository of silly meme images you can share freely, giving public access to it (it's still locked behind an account for upload and general access) isn't that much of a security concern and then your public links should work just fine.

If you want something that is more of a social media site and image gallery like Imgur is, maybe Immich can handle some of that, but if your goal is simply sharing image file links, I'd focus on looking for things that are more for sharing files, since images are just files and it doesn't sound like you need all the complex image-specific handling really.