Except the second one is only useful if you actually do have another offer, so the two are not equivalent.
What you should actually do is politely request that you be allowed to work remotely, as you "realized that you are not looking forward to spending a significant chunk of your day commuting, and have realized that remote work is much better for your mental health". This is still a polite request, but fairly clear that you'll probably start looking for another job if they deny.
What you should actually do is politely request that you be allowed to work remotely, as you "realized that you are not looking forward to spending a significant chunk of your day commuting, and have realized that remote work is much better for your mental health". This is still a polite request, but fairly clear that you'll probably start looking for another job if they deny.