One reason why La Terminal doesn’t encourage tmux for session preservation or mosh is their low fidelity terminal rendering, so I use a tiny “keep the session open” instead. It is a small binary I bundle with LaTerminal.
To get the best of both worlds, I cooked my own “tmux” built on top of headless SwiftTerm, so I get high fidelity rendering - but deploying it seems like an uphill battle: