From my investigation and reading a lot about this, it seems like the transaction is just removed and the ether returns back to some address. With Bitcoin, orphaned blocks are initially accepted by the network, but will be rejected once a longer blockchain is received that doesn't include the block. Is the same thing true in Ethereum?
The behavior in Ethereum is the same as in Bitcoin. At first the transactions seem to have gone through, but after a better chain is found it is as if the txs never happened.
Not true. The transaction gets back to pending state, it is not cancelled. Now, if another transaction from the same sender and with a higher nonce was accepted by then, then the first transaction will be effectively cancelled but because of the nonce, not because of the block being orphaned. Dec 26, 2019 at 1:44
According to Ethereum White Paper transactions of orphan (uncle) will be added to the chain anyways.
As described by Sompolinsky and Zohar, GHOST solves the first issue of network security loss by including stale blocks in the calculation of which chain is the "longest"; that is to say, not just the parent and further ancestors of a block, but also the stale descendants of the block's ancestor (in Ethereum jargon, "uncles") are added to the calculation of which block has the largest total proof of work backing it.
I don't think you're answering the original question, but another one. The OP is asking what happens to the transaction in terms of whether it affects the Ethereum state ("... ether returns back to some address"). Your answer explains that the uncle block is included in the POW calculation. However, since the uncle is not an ancestor of the active tip, its transactions can't have been involved in transitioning the state. Nov 21, 2020 at 2:06