FluidApp can't save passwords.
MacPin looks interesting! Thanks, will check it out. However, Safari-based browsers have a horrible show-stopping flaw; they don't (yet) support pasting images into web applications. This is why I love Safari for browsing and reading, but can't bear to use it for JIRA, GitHub, etc.
In Chrome (and thus Epichrome), you just hit your screen capture shortcut (Cmd-Shift-Ctrl-4 by default on macOS), select a rect of the screen to copy, and paste. Boom! Your bug report or GitHub comment now has an image pasted into it.
In Safari, you have to hit your screen capture shortcut, open Preview or similar app, create a new image, save it as a file, then go back to the web app and upload the image.
There's something deeply, horrifically wrong with that workflow.