There's quite a few videos recently, here's two more that I've watched.
Here's a video by Invicta which shows several campaign mechanics, the research tree as well as some battles including a siege and an attack on an iron mine.There's also this one that I recommend watching. Done by a channel called Angory Tom, the two players take a... different approach to the campaign which is enjoyable to watch.Invicta's video didn't really impress me with the visuals but, from the second video, it seems like Invicta's playing at low graphics making everything look flat, burry and bland. The visuals look much better in other videos. Some people have been saying the U.I. is a bit cluttered and I maybe agree though there's so many new mechanics I'd have to spend time in person learning what everything is for before really being able to tell.
Combat seems to be quite fast, and heroes are very powerful. Maybe too much so as people are using them very offensively. Early game battles seem to involve mostly sending your heroes to duel, defeating the enemy general then watching the rest of their army flee. Though this apparently is harder to do as armies move beyond militia a get higher stats and moral.
One little detail I like a lot is the flags units carry are sometimes left sticking in the ground when the unit is killed. A nice detail that makes battle locations stand out more.
Sieges work much the same as previous Total War games. Units have grappling hooks to scale walls though you can also build battering rams, siege towers, or even sappers to bring down walls. Something that I've kind of missed from Rome 1.
The A.I. seems to also act a bit better during sieges, retreating to the central square when you breach the walls to defend from there. Apparently the enemy heroes move there as well when you take the walls.
Armies have supplies now, so you need to restock food in your territory or take it from enemy armies if you want to venture beyond your borders for long periods of time.