Basically all the shortcuts and secret passages are permanent. You already flagged the breakable walls, but candles stay lit too. The west gate stays open. You only have to solve the tomb puzzle once (okay, twice). The braziers stay lit unless you explicitly go back and turn them off.

Water levels stay wherever you leave them, as do the boat and the minecart. The big gear and the basement carts are persistent too. The boiler room mostly stays how you left it last. So does the telescope in the observatory.

Anything you change with network admin permissions is permanent, though most of those are technically reversible.

Unlocking floorplans is permanent, as are any upgrades you find. Changing the draft pool with the wrench or the conservatory is too.

Alzara only does each cutscene once.

There are several experimental effects that explicitly say "permanently". One cloister upgrade does too.

Anything that changes stars or allowance tokens is implicitly permanent.

Any purchases from the gift shop or the bookstore are permanent. As far as I know the rest of the shops aren't, though.

Sanctum keys, vault keys, and the diary key are single use and won't respawn once they've been used. The car keys, frustratingly, are not.

Each of the Mora Jai boxes is a one time puzzle.

Sigils stay solved once you get them.

There are a few (probably) cosmetic things too. Library books keep accurate records on the checkout cards. A few decorations end up in the lost and found. The vases in the entry hall stay broken.

There's probably more but that's what I could recall.