I choose, wich champ is in my arena team. I choose, in wich turn order they act (by speed on their equip).
You wouldn't notice if it's a bot team or not when you attack because the whole Raid is a turn-based game you play via internet. You wouldn't even notice if it is a real player or a bot if there would be "live PvP", similar as you don't know if your opponent in any turn based strategy game, for example, chess, is a bot or not.
Indeed you do choose your team, just as someone at Plarium chooses what champions to put in a dungeon stage. That does not mean that doing the dungeon is you doing PvP against said Plarium employee. You build your defense team and that's where your interaction for that ends. You don't build it against a specific opponent, you build it based on pure statistics to minimize the number of enemies that will be inclined to pick a fight against you. You build your offense team and pick a team to fight against when attacking, and that's pretty much the only point of interaction you have for that, which is not really any different from picking a team to clear a dungeon though in this case a dungeon with a random, pre-determined composition of opponents in them. You may technically be fighting against a player-made team, but saying that one is PvE and the other is PvP is a distinction without a difference. You're doing that everywhere in the game. You're not interacting with another person, you're interacting with a scripted sequence of events strictly one-way. Of course, it doesn't make much of a difference either way. In many matches, you won't even get an opportunity to do anything before it's over, and even in the ones you do there's not really that much viable variance possible.
In the end, it's not really about what you call it, but the fact that it's functionally identical. Personally, I'd never call anything PvP unless it has direct interaction between two players, where both have an opportunity to influence the outcome in a meaningful way. In Raid where this only happens when one player picks another team to fight, it is not sufficient. Whether it could still be PvP or not with an AI sophisticated enough to be indistinguishable from a human player is an interesting philosophical debate however.