I ride a similar distance (6-16 miles RT, depending on the switchover point), and am still quite new at this as well. I offer my experiences, not advice.

I switched out MTB tires to somewhat aggressive 'urban' tires (but puncture-resistant) last year. This year, I went to a lighter weight smooth tread tire, and lighter weight tubes, and gained about 0.7 mph immediately.* That cut my time down, and I felt less sweaty as a bonus.

The lightest clothing (warm enough to start, but maximize cooling during the ride) means I don't have to slow down as much the last few miles; I do swap shirts once I get to the office.

Replacing the chain (old one was dirty and stretched), and keeping it clean feels much smoother, vibrates less. Not sure how much it helps.

I use toe clips, as it helps me keep my feet on the pedals as I go over potholes and storm drains; I am not quite comfortable with clipping in, and I bike in with my work shoes. Works for me.

I go much faster on my road bike, and on weekends I go much faster because I ride on country roads with (almost) no traffic lights, or even stop signs. Getting in at least one more demanding ride on the weekends seems to pay off, as I can pay attention to cadence, fit, shifting, etc.

My shortest route also has the most lights, and hills, so isn't necessarily the fastest route.

*I also started carrying a spare tube, instead of just a patch kit, as I figure the chances of a flat are probably several times higher.