Is your employer a government agency like a school or university? If so definitely put money in the 457(b) unless the investment options or fees are truly terrible. If not, the plan is subject to the creditors of the institution so I would be inclined not to do it, especially if it's a university and/or hospital as we're in strange times for both those institution types right now. If the institution is financially strong enough, you'll be leaving soon enough, and your potential tax savings (difference between current marginal rate and marginal rate when you leave and withdraw) is large enough then I might consider a non-governmental 457(b), but I'd be much less inclined to. The limit is separate from the 403(b).
I'm pretty sure the mandatory 403(b) contribution doesn't count towards the employee salary deferral limit ($19.5k in 2020 and 2021). This might not be universal, but I know it's true of my wife's plan. Or do you mean your mandatory contribution plus your employer contribution hits the overall limit ($57k in 2020, $58k in 2021)?