Running $(atuin init bash) is simply wrong. You need to run eval "$(atuin init bash)". The error “-bash: __atuin_bind_ctrl_r=true: command not found” is unrelated to the original problem, but it is caused by the way how atuin init bash was called.
They bind up (ESC [ A) and down (ESC [ B) to the history search commands. So if your alias file is loaded after eval "$(atuin init bash)" is executed, the Atuin keybindings for up/down are overwritten. You need to disable these keybindings (as you solved), or you need to make sure eval "$(atuin init bash)" is executed after these keybindings.