How much energy is lost with a gravel tire compared with a road tire?

I understand that around 20% of the energy while cycling is lost by the deformation of the [tires]

No not really. Rolling resistance will increase linearly with velocity while drag increases with the cube of velocity, so rolling resistance is not a fixed percentage of total power lost. At higher velocity drag will completely dominate.

use plain tires (no tread pattern) as these tires will get more contact area with the ground, therefore needing less deformation in order to equilibrate the forces (with F=P/A)

That's not completely true. The tire carcase is is somewhat stiff and each tread block contacting the ground supports an area greater than its own cross section area above it. Because the forces are concentrated down trough the blocks the area actually in contact with the road is lower but each block exerts a higher pressure against the road surface.

There is additional power loss through greater flexing of the tire and tread blocks though so there is additional power loss compared to a slick tire.

A factor I don't think you have taken into account that gravel tires are typically wider than road tires and run at a lower pressure, which leads to higher rolling resistance.

I can't point to formal research but the Global Cycling Network YouTube channel has some some tests.

They ran with a power meter, on rollers:

1. 28mm GP 5000, 90 PSI, 45 KPH 299W
2. 28mm GP 5000, 70 PSI, 45 KPH 327W
3. 40mm Terra Speed 70 PSI 45 KPH 449W
4. 40mm Terra Speed 40 PSI 45 KPH 516W

The deltas were significant.

Now based on that, I was wondering if there is any estimate on much gravel bike tires (with some light tread pattern) might contribute to the loss of energy compared with road bike tires (plain) for the same conditions (dry, plain and smooth road).

You don't need to estimate. You can measure.

For example, here's one gravel tire: https://www.bicyclerollingresistance.com/cx-gravel-reviews/panaracer-gravel-king-sk

Its rolling resistance at high pressure is 21.7 watts per tire for a load of 42.5 kg and speed of 29 km/h. If the total bicycle load (bike + rider + cargo) is 85 kg, you get twice this or 43.4 watts.

In comparison, the most reasonable road tire today is probably the Continental Grand Prix 5000 in 32mm width: https://www.bicyclerollingresistance.com/specials/grand-prix-5000-comparison

At 100 psi, it loses 9.7 watts when used with butyl tubes. If you think 100 psi is too much for 32mm, you can pick the 28mm width (10.3 watts) or reduce pressure of 32mm tire to 80 psi (11.0 watts).

So a road tire uses at most 11 watts per tire or 22 watts total.

Therefore, you lose at least 21.4 watts when using gravel tires.

Is this much? A quick simulator (taking into account riding uphill, on level ground and downhill in approximately correct proportions and simulating the uphill resistance, rolling resistance and air resistance) I wrote in Matlab shows that with the 21.4 watts extra rolling resistance, your average speed reduces from 22.4 km/h to 21.1 km/h. The simulator assumes the rider produces 90 watts on level ground, 180 watts on uphills and 0 watts on downhills.

I'd say this is much. For example, in 10000 km distance, you lose 27.5 hours when using gravel tires.

If you assume a pair of road tires costs 80 EUR and lasts 10000 km, you have to pay only 2.9 EUR per saved hour.