The Edit Screen can target any table, including the user table. You may not be able to direct to it through the ‘user profile’, but you should be able to get to the ‘user table’. All you need is a single relation or a single value → whole row in whichever table is the source of the screen that contains the action to open the edit screen. You should be able to open it through that relation.
Edit Forms and Detail Screens are tightly integrated with the table. They can’t be independently designed when opened from multiple locations. You build it once and it’s used everywhere. An alternative to Detail screens is to use New screens for independent designs, but we don’t have that same option with the Edit form.
A couple of options:
Instead of an Edit form, use ‘Show New Screen’ → ‘This Item’ to get a separate screen linked to the same row. It will be updating values in real time.
Another option is to use the same Edit form, but use a custom action to first set a value in the user profile and then use that value to determine which components are visible on the edit form.
You can set up a custom form, but it’s a bit more setup. I do use a reusable custom form that can add or edit rows. It does require a custom action to set a mode (Add/Edit) and clear or prefill user specific columns before opening the form, based on the mode that was set. The button to submit the form either adds a new row or updates an existing row through a single relation based on the mode that I have set. It’s a bit involved to get into details here. It’s a little more than you are asking for, but it could be set up just for editing and the mode would control which components are shown. Probably overkill for what you are looking for though.
For future reference, if updates count is a problem, then you can leverage having two types of edit screen through the type of screen you open.
I have that setup in an app months ago, one button opens the edit screen on an overlay, one opens it with a slide in. The slight difference in the URL of those screens can be what you need to construct visibility conditions.