have you tried/considered kitty as your shell? not the PuTTy clone, the one by calibre dev.
I like it because it essentially has a built in terminal window tiler, though i still use tmux with kitty, I reserve tmux for when I need a command/process to run in the background, or to continue to run if I accidentally close/quit the window/app.
I personally prefer kitty as my terminal and fish as my shell, customized with the `es` theme from `oh-my-fish` and `pisces`, an auto-pair for brackets, parens and quotes. very minimal prompt that stays out of the way yet is informative when in a git dir, ssh or failed command.
though I often distro hop on a test laptop, I am beginning to like `st` though `kitty` is great "out of the box"