Ships can move almost at will everywhere (We once meet one basking in the corona of a star) and this very fast. Effectors allow to 'hack' less powerful or sophisitcated ships. Since there's hardly any cover in space, it doesnt matter if the weapon is 'displacing' some antimatter into your foe via targeted wormwhole or some FTL-hyperspace laser like thing or an (FTL, hyperspace) missile. What matters is wether the target has the fields to fend this off. AFAIK in the culture-verse, ships engines that propel them through hyperspace and fields are linked on a deep technological level, so if a civilsation masters one it will be good at the other.
For battles in deep space there's not much scope for tactics, the combination of better engines, fields, weapons and effectors wins (Unless of course one side gives their ship to one of those meatbrains). Decisions to be made are whom to shoot first, and with what. I think this is what we see in the novels.
There are exceptions, near the ends of Hydrogen Sonata and Matter ships use physical structures that extend into hyperspace to some effect, IIRC in Consider Phlebas some unarmed culture ships hide in stars coronas or so because their enemies can't follow there because of inferior field technology.
To your specific question, "In particular I'm interested in the tactics made possible through breaking general relativity, as we understand them":
Again, no new tactic. Breaking relativity means there's no absolute speed limit on anything, speedds of communication or travel are purely contingent on the technology available.
So in the end, in the Cultureverse there's no real scope for clever tactics but for one grand strategy: Be the technologically most advanced civlization around, with the best engines, fields effectors and Minds. Which boils down to have the best Minds, who will develop the other things and even better Minds. It is a testament to Iain M. Banks storytelling that he built a universe where history is driven by anonymous progress and excentric Minds, and still tell relatable stories where all meatbrains and other people matter.