Hi Jocelyn,
From what I can tell trying to do the same thing, no masking isn't an option on a standard feature service.
However, depending on your licencing level (hopefully someone can verify what level is needed) you can create "view layers" from the feature layer overview.
These can then be filtered by fields or geographical area from within the classic web map viewer, from what I can see there's no functionality for it in the new map viewer.
All that being said, you can only do this with your organisation's layers at best, something like living atlas data cannot be used. And you have to do this for each individual layer within a feature layer, which get's pretty dull after 3/4 layers. The ability to set a geographical display area or use a mask layer in the webmap would make this so much easier.
Hope that helps you out a little!