So what is the purpose of the non-solicitation agreement? Like most, does it prevent you from approaching your former customers with an offer of a new service provider?

Are you in sales for your new company? If so, this may certainly affect your ability to perform your duties if your duties include soliciting new business. If however you are in a service role and go to calls assigned to you, or your company has sales reps that contact potential customers including your former clients, then there should be no issue depending on the wording.

Personally I'd be more concerned with a non-competition clause.

Seek legal counsel so that you know exactly what you have and how it may affect you.