The bonus attack speed provided by placing a relic into the docks for Holy Roman Empire appears to affect all warships (including those of opponents).
Currently running game 5.0.7274.0, first noticed this in a skirmish match against AI. The attack speed in the tooltips for the enemy ships were updating to show reduced/increased attack speed as I placed and removed the relics from my own docks.
Did some tests in a 1v1 skirmish against another player and the actual attack speed bonus did apply to both of our ships so it isn’t just a tooltip error.
We each had a galley attacking an outpost on the same screen and the attacks remained synchronized when adding or removing relics from my docks. We could both see the attack speed changing in the tooltips and the attacks were going faster and slower as relics were removed/added, so it’s pretty clear it was actually affecting both ships.
The skirmish match was Holy Roman Empire (myself) versus English (with both the AI test and player test). For the player test, we used Galleys only to attack Outposts. Did not check other warship types.
I do note that the dock relic buff doesn’t specifically state that it affects player or ally ships only but surely this is not the intended functionality.