Yup. Multiaccount is desperately needed in Element. Other Matrix clients (FluffyChat, Quaternion, possibly Nheko?) have it already though)... plus you can always cheat and just open Element in multiple browser tabs :)
Works surprisingly well for my use-case (keep work stuff separate on Element) and even allows me to disconnect completely from work by simply turning off the profile.
[1]: https://github.com/PeterCxy/Shelter
Edit: added note about using Android
... but it's quite far from actual multi-account support, so I do think that's still necessary :)
It's either obtrusive to the UI, or completely hidden.
Stack accounts at the OS level, or close to it.
Your advice to run a separate browser tab is by far the best — even if on mobile.