This use of ever would indicate "always" in this context. It sounds a bit archaic.
• adverb 1 at any time. 2 used in comparisons for emphasis: better than ever. 3 always. 4 increasingly; constantly: ever larger sums. 5 used for emphasis in questions expressing astonishment: why ever did you do it?
It is, on a higher level, the same challenge health care workers forever faced.
Not really grammatical. You could use "forever" if the sentence was rephrased "...workers have faced for ever" [[for a very long time]] or "...workers forever face" [[continually]].
• adverb 1 (also for ever) for all future time. 2 a very long time. 3 continually