How to effectively use quick battles (autobattles)?

I suspect that (as someone mentioned here earlier), the quick battle calculation algorithm doesn't take into account the presence of the Tactics skill and the level of proficiency in it.

That's incorrect.
I won't go into details, but if a quick battle lasts longer than 30 rounds, it switches to a battle calculation similar to an AI vs. AI battle, where mana is already considered spent, and the troops return to their initial state.
There are also a couple of bugs in the quick battle (actual bugs, not just "oversights") - with flying creatures, with the resurrection of phoenixes, but they have been fixed in the HD mod. With the exception of the above, the quick battle is identical to a regular battle.