Having the app enabled is being on-call for potential assignments, not actually working. In my youngest years, I did that for multiple temp agencies at the same time a lot. Are they employees of both? Sure. Multiple W-2 employers is not that uncommon for people doing temp work.
> How should benefits be calculated?
In most cases, they will probably work little enough for each as to not reach mandatory benefit eligibility under most employer mandates.
> If I am an employee of a company, they are probably not going to let me work for a competitor while I am on the clock with them.
If you are an employee of a company giving on-demand assignments, they probably aren't going to consider you on the clock merely because you have indicated you are available to take an assignment if it becomes available.
If there are minimum paid shift rules in play, they may consider you on the clock and demand exclusivity for the paid period once you accept a job, even if there is a lull between assignments, though.