DSK release notes published, so main phase changes can be fully researched now:
https://magic.wizards.com/en/news/feature/duskmourn-house-of-horror-release-notes

Related article about phase changes and card examples: https://mtgrocks.com/postcombat-main-phase-change/

• Cards like [[Aggravated Assault]] must add additional main phases, not first/second (already supported). There are 8 cards with additional main phase effects.

• Make sure cards like [[Chancellor of the Tangle]] trigger one time per game. Old rules text “first main phase” replaced with “first main phase of the game”. There is only one card with such texts and looks like it must be fixed.

• Refactor all triggers with EventType.POSTCOMBAT_MAIN_PHASE* and EventType.PRECOMBAT_MAIN_PHASE* to check “not extra”.

I don’t think it requires any code renaming from precombat to first and post combat to second. Official rules still use it, see “505. Main Phase” (from blb update). Maybe will be changed in later rules release (with dsk).

Aggravated Assault - (Gatherer) (Scryfall) (EDHREC)

{2}{R}
Enchantment
{3}{R}{R}: Untap all creatures you control. After this main phase, there is an additional combat phase followed by an additional main phase. Activate only as a sorcery.

Chancellor of the Tangle - (Gatherer) (Scryfall) (EDHREC)

{4}{G}{G}{G}
Creature — Phyrexian Beast
6/7
You may reveal this card from your opening hand. If you do, at the beginning of your first main phase of the game, add {G}.
Vigilance, reach

• Refactor all triggers with EventType.POSTCOMBAT_MAIN_PHASE* and EventType.PRECOMBAT_MAIN_PHASE* to check “not extra”.

Worth noting: Not everything is being changed away from "postcombat main phase", but they still haven't reverted the errata yet on Neheb to make it still function during extra main phases:
https://x.com/WotC_Matt/status/1816524550433329385

So we still need to wait for them to finish up the Duskmourn updates to find out exactly which 11 cards, besides Neheb the Eternal, Brazen Cannonade, and Megatron, Tyrant, are still getting to work during extra postcombat main phases.

Update: we now have a list of all the cards that will still say "postcombat main phase"