On a desktop, you can use KeePass and its variants to "auto-type". It'll switch focus to the last app you were in and type your username, a tab, your password, and then enter. No extensions or clipboard required. Just hit CTRL-SHIFT-V after highlighting the entry.
I tried using this but the final "enter" made me too uncomfortable. I really wish it was optional so I could verify where it just typed the password before submitting. After accidentally sending my password in the wrong field/window a couple of times I stopped using it entirely. Now I just copy-paste :(
keepassxc has extra options in the auto-type menu for "username", "username<enter>", "password" and "password<enter>" in addition to the normal "username<tab>password<enter>"
It looks like paste and it's almost the same from the user perspective, but the data never makes it to the clipboard, where it would be available to every running application.
Use a browser extension. For example, the 1Password extension uses (authenticated) IPC to talk to the app and then injects the password into the DOM directly.
Gfycat already generates memorable URLs so it’s definitely possible. I myself do it manually nowadays (ie generate phrase password to be stored in manager so I can copy it manually if needed)