Steelworker's nor Steely Spirit's Bulbapedia page make any mention of interacting with each other. It is important to note that the abilities do effectively different things. Steelworker multiplies the damage done by a Steel-type move by 1.5, while Steely Spirit multiplies the base power of the Steel-type move by 1.5.
However, Steely Spirit's boosts do stack when multiple Pokemon on the field have exclusively Steely Spirit. (See "Effect" category in link above.)
Hope this helps!
No, they don’t cause a Pokemon can’t have two abilities,and it only boosts the power of the Pokemon with those abilities
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