Earlier quoted context omitted.
First, I'm responsible for handling my clients' data, such as their email addresses or phone numbers. It doesn't matter that they're business customers rather than consumers. GDPR still applies. Secondly, though not always the case, I might have to process their respective customers' data in some way in order to do my job (by having access to a production database, for example). So, yes, GDPR absolutely does apply to…
So you're saying that you are asking consent to store the phone number and email address of a client? And you'll provide clients with the right to be forgotten, meaning that you're prepared to delete their contact information? This seems like overkill.
No, I didn't say that. GDPR doesn't mean that you have to ask for consent in each and every case. If as a business you have a legitimate interest to store client data for a specific purpose you don't have to ask for explicit consent. Being able to contact clients in the future who contacted you first constitutes such a legitimate interest.
As for the right to be forgotten: Sure, why wouldn't I? If they don't want to be contacted anymore and want me to delete their contact info I'm happy to oblige.