Because you

still think that I have performed my job honestly

you are rightfully

not sorry that I sent that email

You did your job and you did it well. I wanted to stress this just to clarify that you do not owe her telling her that you are sorry for the way it all turned out, especially - and above all - because

her Manager decided that she should be given a written warning

So, the best you can do to be "empatic" with her is stressing the same clarification I stressed above, so that she clearly understands that you were just doing your job, you did it well, and if there's someone who made her feel bad in the end it is her manager (whether he too did his job well or not). This way you are being totally fair to her, even more than fair. Whether she understands and accepts your position (reads: being mature), at this point, is no longer within your power, there's nothing you can do more than doing your job well and even showing yourself to be a caring person.

That being said, to answer your other specific questions:

• whether your other coworkers will trust you or not depends on - again - how much they are willing to accept you doing your job well and being a caring person (again, reads: being mature);
• whether she is going to make something big out of this up to the point where future interactions are difficult, well, it will depends on her level of maturity, still out of your powers;
• conveying how you feel is best conveyed by simply stating the pure truth;
• misinterpreting what you say, in this case, would be, wait for it... lack of maturity;
• yeah, a single simple conversation where you tell her the truth and the way you feel must be more than enough;

I repeat: you did your job well and you even went beyond that by being willing to tell her you are empathic to what she feels... if she (or any other coworker) does not acknowledge and accepte this, I'm afraid you are dealing with someone lacking adult maturity.

My 2 cents, of course.

Because you

still think that I have performed my job honestly

you are rightfully

not sorry that I sent that email

You did your job and you did it well. I wanted to stress this just to clarify that you do not owe her telling her that you are sorry for the way it all turned out, especially - and above all - because

her Manager decided that she should be given a written warning

So, the best you can do to be "emphatic" with her is stressing the same clarification I stressed above, so that she clearly understands that you were just doing your job, you did it well, and if there's someone who made her feel bad in the end it is her manager (whether he too did his job well or not). This way you are being totally fair to her, even more than fair. Whether she understands and accepts your position (reads: being mature), at this point, is no longer within your power, there's nothing you can do more than doing your job well and even showing yourself to be a caring person.

That being said, to answer your other specific questions:

• whether your other coworkers will trust you or not depends on - again - how much they are willing to accept you doing your job well and being a caring person (again, reads: being mature);
• whether she is going to make something big out of this up to the point where future interactions are difficult, well, it will depends on her level of maturity, still out of your powers;
• conveying how you feel is best conveyed by simply stating the pure truth;
• misinterpreting what you say, in this case, would be, wait for it... lack of maturity;
• yeah, a single simple conversation where you tell her the truth and the way you feel must be more than enough;

I repeat: you did your job well and you even went beyond that by being willing to tell her you are emphatic to what she feels... if she (or any other coworker) does not acknowledge and accepts this, I'm afraid you are dealing with someone lacking adult maturity.

My 2 cents, of course.

Because you

still think that I have performed my job honestly

you are rightfully

not sorry that I sent that email

You did your job and you did it well. I wanted to stress this just to clarify that you do not owe her telling her that you are sorry for the way it all turned out, especially - and above all - because

her Manager decided that she should be given a written warning

So, the best you can do to be "empatic" with her is stressing the same clarification I stressed above, so that she clearly understands that you were just doing your job, you did it well, and if there's someone who made her feel bad in the end it is her manager (whether he too did well his job or not). This way you are being totally fair to her, even more than fair. Whether she understands and accepts your position (reads: being mature), at this point, is no longer within your power, there's nothing you can do more than doing your job well and even showing yourself to be a caring person.

That being said, to answer your other specific questions:

• whether your other coworkers will trust you or not depends on - again - how much they are willing to accept you doing your job well and being a caring person (again, reads: being mature);
• whether she is going to make something big out of this up to the point where future interactions are difficult, well, it will depends on her level of maturity, still out of your powers;
• conveying how you feel is best conveyed by simply stating the pure truth;
• misinterpreting what you say, in this case, would be, wait for it... lack of maturity;
• yeah, a single simple conversation where you tell her the truth and the way you feel must be more than enough;

I repeat: you did your job well and you even went beyond that by being willing to tell her you are empathic to what she feels... if she (or any other coworker) does not acknowledge and accepte this, I'm afraid you are dealing with someone lacking adult maturity.

My 2 cents, of course.

Because you

still think that I have performed my job honestly

you are rightfully

not sorry that I sent that email

You did your job and you did it well. I wanted to stress this just to clarify that you do not owe her telling her that you are sorry for the way it all turned out, especially - and above all - because

her Manager decided that she should be given a written warning

So, the best you can do to be "empatic" with her is stressing the same clarification I stressed above, so that she clearly understands that you were just doing your job, you did it well, and if there's someone who made her feel bad in the end it is her manager (whether he too did his job well or not). This way you are being totally fair to her, even more than fair. Whether she understands and accepts your position (reads: being mature), at this point, is no longer within your power, there's nothing you can do more than doing your job well and even showing yourself to be a caring person.

That being said, to answer your other specific questions:

• whether your other coworkers will trust you or not depends on - again - how much they are willing to accept you doing your job well and being a caring person (again, reads: being mature);
• whether she is going to make something big out of this up to the point where future interactions are difficult, well, it will depends on her level of maturity, still out of your powers;
• conveying how you feel is best conveyed by simply stating the pure truth;
• misinterpreting what you say, in this case, would be, wait for it... lack of maturity;
• yeah, a single simple conversation where you tell her the truth and the way you feel must be more than enough;

I repeat: you did your job well and you even went beyond that by being willing to tell her you are empathic to what she feels... if she (or any other coworker) does not acknowledge and accepte this, I'm afraid you are dealing with someone lacking adult maturity.

My 2 cents, of course.