I not understood this one, both miners with get full reward 'temporarily'
Part of the network will accept Block A, and part of the network will accept Block B. The part of the network which accepts Block A will see the coinbase transaction which sends the block reward (6.25 BTC subsidy + fees) to Miner A. The part of the network which accepts Block B will see the coinbase transaction which sends the block reward to Miner B. Both Miner A and Miner B will, according to different parts of the network, have received the block reward for their blocks at the same height.
Once either Block A+1 or Block B+1 is found, then the entire network will switch to the winning chain. The block which is not built upon will be discarded, and so the coinbase transaction which rewarded that miner will no longer exist.
the nodes will choose the block that has the most proof of work, which means the block with the longest chain of valid blocks leading up to it. this is because the longest chain represents the most computational effort (i think hashrate is it right?), and therefore the most secure chain.
This is sort of correct, but the terminology is poor. First, it is not necessarily the longer chain, but the chain with the most work. These are usually the same thing, but not necessarily so. Also, nodes can't choose a "block that has the most proof of work". Two blocks mined at the same height as in this scenario both have the same amount of work. The chain split will be resolved when a new block is found on top of one of those two competing blocks. Only at that point will one chain have more work (in the form of one additional block) than the other chain and therefore be the main chain which all nodes will converge on.
once one of the blocks is added to the blockchain, the other block becomes an orphan block, and the transactions included in that block are returned to the mempool. The miner who mined the orphan block will not receive a reward, and their computational effort will be wasted.
As I explained above, orphan block is the wrong term here, but lots of people use it by mistake. But yes. Once one of the blocks is built on top of, then the competing block is discarded and becomes a stale block. Any transactions which were in this discarded block but were also in the mined block will just stay as confirmed. Any transactions which were in this discarded block but were
not also in the mined block will return to being unconfirmed.