What makes one bike faster than another when same wattage is applied?

Weight doesn't make much difference unless you're climbing, but aerodynamics does, and so do tyres, but less so. Assuming both drivetrains are in good condition, they'll be similarly efficient, differing mainly in weight and possibly shifting speed. Fit is also important for your efficiency.

One bike is a more aerodynamic frame, but it's reasonably likely that it also puts you in a more aerodynamic position. This would mean a noticeably increased drag, but the thing about drag is you don't really feel it, you feel wind speed. A more aggressive position may help, as may clip on aero bars, but don't spoil the fit

Faster rolling tyres do help, but you have to make a significant improvement to notice it. There are rolling resistance figures for many tyres available online, with notes on how to apply them

Most likely aerodynamics. Modern road bike vendors spend a lot of money improving the aerodynamics, especially for the racing top models. Mor for the so-called aerobikes, but even for the ultra=light bikes, up to the point the weight permits.

The weight is not too important on the flats and is less important than many think even in the hills as most of the weight is in the rider anyway.

Tyres will make some of the difference too. Obviously, top ricing tyres will be faster on smooth tarmac. I made a big improvement from the stock Schwalbe tyres to better G-Ones on my gravelbike. But aerodynamics of modern bikes cannot be beaten by tyres, the differences are usually smaller there.

The groupset may be more clumsy when shifting but when the gear is there, it does it job very well. If you want more gears and have the money (which you probably have if you have the Cervélo S), you can buy 105, it will be lighter, but do not expect to be any faster on flats. (I ride Claris regularly. Some would miss the gears, the shifting requires some power in your hands, but otherwise it does the job done well enough.)

For others' reference, the Cervelo S-Series is an aero road bike. The OP didn't state a model year, but the current generation S-series bikes all appear to have aerodynamic carbon wheels and fully internal cables. If the OP did indeed pay over US$7,000, then it seems like they have an S5, which may have some additional integration at the front end of the bike (handlebars, cabling, fork), which might improve the aerodynamics further.

In contrast, the Trek Domane is an endurance road bike. The Al2 is an entry level version.

In general, if we are talking about a bike's speed for a certain input power, aerodynamics should have the biggest impact, then rolling resistance, with weight being a distant third. Furthermore, weight mainly applies uphill.

Additionally, the placebo effect can't be discounted. This is not to say that the OP alone is gullible. It is rather that we are all gullible in unblinded tests between different products. The 3.5 lbs additional weight of the Domane alone would exert a nocebo effect (opposite of placebo), even if the objective impacts are relatively small unless you are on a steep climb. The groupset should also fall into this category. Provided the OP has enough gears to maintain their optimal cadence at most speeds, the groupset alone shouldn't actually make the Domane substantially slower. That said, Claris does only have 8 cogs, and the Domane's stock 11-32 cassette could have substantial jumps in gearing. Notably, the gearing is 11-13-15-18-21-24-28-32. On flat ground, I use the 13, 14, 15, 17, and 19 cogs a lot, and I frequently wish I had a 16t cog for more even gearing changes in that range. Claris' gearing jumps in that gear range are significantly larger.

Upgrading the Domane to racing tires and light butyl or latex tubes would definitely make a noticeable difference, and would be cost effective. If the Domane used disc brakes, you could potentially share the wheelsets, but the Al2 appears to be rim brake. Extensive upgrades to entry level bikes are not cost effective. If you want a fast endurance bike, then it's better to buy one from the start.

In a steady-state effort on level ground, there are three forms of resistance that you need to overcome. In order, these are:

1. Aerodynamic drag
2. Rolling resistance
3. Mechanical losses

This page does a good job visualizing these.

Say, for example, that you need to produce 200 W to go 20 mph.

A good drivetrain in good tune can be 98% efficient, which is amazingly good. Even your Claris drivetrain is probably 95% efficient, unless it's dirty and the parts are worn out. There's not a lot of room for improvement there. This is soaking up maybe 5 W, maybe less.

Tires account for rolling resistance (weight figures in too, but the difference between you + heavy bike vs you + light bike is probably about 5%). Good tires might soak up 30 W. Bad tires can be considerably worse in terms of rolling resistance: a really fast tire might use only a quarter the power that a really low-quality tire would use.

That leaves aerodynamic drag soaking up the other 165 W. And what makes aerodynamic drag especially important is this: mechanical losses and rolling resistance scale linearly with speed, but aerodynamic drag scales in proportion to the third power of your speed. So going just a little faster requires a lot more energy; conversely, improving aerodynamics a little can have an outsize effect, and that effect gets magnified the faster you go.

Another thing to remember is that the biggest source of aerodynamic drag is probably you, not your bike. Two bikes could have about the same aerodynamic drag if you put them in a wind tunnel with no rider, but if one puts the rider in a more aerodynamic position, that system will have lower drag.

Also, FWIW, a bike can "feel faster" without really being faster. Deep-section aerodynamic rims are provably faster than lightweight box-section rims, even up moderately steep grades. But pulling away from a dead stop, you can feel the lighter wheel "spin up" more easily.