How do pokemon feel when they are traded away? Do they feel abandoned by their original trainers or is it something that would (or should) be discussed beforehand?

It depends on how close you were before the trade, the pokémon’s temperament, and whether or not you’ve made your intentions clear with your pokémon first. For example, if you’ve abruptly traded away a pokémon with whom you’ve bonded, then yes, they may develop trust issues or become resentful, which will require their new trainer to work on building a relationship again. Other pokémon, particularly those who might not have been agreeable to you before the trading process or with whom you haven’t bonded, might be happier with a different trainer, to put it bluntly. If they notice at all.

Speaking to your pokémon beforehand can indeed help reassure them and adjust to their new trainer or at least understand why the trade is happening, but some pokémon may react negatively to the trade regardless. If the receiving trainer puts forth a lot of effort in bonding with their new pokémon immediately, however, these feelings can often be alleviated rather quickly.

Finally, interestingly enough, the exception to the above are pokémon with trade-based evolutions. Many trainers who trade to evolve often engage in “trades and trade-backs,” or agreed swaps between trainers with other pokémon that evolve via trading. Pokémon whose evolutionary requirements involve trading often understand by default that the process is necessary for their well-being, and the practice is so commonplace (and often outlined between all involved parties, including pokémon, beforehand) that they are also aware that the swap is temporary. Thus, they tend to mind less, and if the trade ends up being permanent—as in, they never return to their original trainer—then they’re often so focused on adapting to and training their new forms that they hardly feel anything at all regarding the departure from their former companions, especially if the receiving trainer is well-prepared to train their evolved selves. Of course, this also means it tends to be harder to bond with newly trade-evolved pokémon (as they tend to be too distracted to notice their new trainers), but with patience and care, it’s not unheard of for these trainers to achieve a level of closeness with their new pokémon.