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OK my Head of HR professional advice. Your company are concerned, they want to reinforce the confidentiality agreement. You should ask yourself the following
1 Would signing this compromise you in a professional capacity in any way or limit your ability to carry out your job, and I mean in reality not in a "can i find a really unlikely scenario where it would cause an issue".
2 Is the meaning of the supplementary doc dramatically and explicitly different to your employment contract? I am going to guess no but it may be more thoroughly worded with the same meaning.
If the answer to the above is a "no" I would sign it and give them the reassurance they are looking for as a happy ex-employer may some day be of use to you. Your soon to be ex employers are just looking for some assurance that you are not passing on pricing info and intellectual property that may render them redundant to your new employer.
Confidentiality agreements are very hard to enforce unless you very deliberately and overtly break them and leave an audit trail of evidence on email or documents behind you.
Do you have to sign it, of course not, but if it's not a big deal then I would and I would say something along the lines of "My integrity is assured but I understand your concerns so am happy to agree to these terms".
If you have a good reason not to sign it I would go with "given the commitment I made to confidentiality/non-compete when I signed my employment contract I think you (the company) have sufficient legal recourse should anything untoward happen, however I can assure that you will not happen as I am a professional/mountain biker and our word is our bond" You may not need the last bit about mtbrs.
In addition your role may have changed since you were initially hired and you may have access to customer pricing and unique ip that they did not envision at the beginning and they may be concerned that revenue or additional work will come under threat.
I would be surprised if there was not a clause about going to work for clients in your contract or that they don't have a clause in place in the customer contract to stop you going directly (they're daft if they don't) or they may have waived that with the client for the ake of goodwill.