How do i transfer domain from one.com to cloudflare by updating nameservers?

Ive read https://developers.cloudflare.com/registrar/get-started/transfer-domain-to-cloudflare/ however i still have questions regarding how this affect other services that my client use from one.com like their emailing service etc. How do i keep their emailing services and other services they might use, intact while only updating the http/https traffic?
Cloudflare Docs
Transferring your domain to Cloudflare tells your registry that a different registrar can now set those authoritative records for you. The relationship is based on trust. Registries only trust one registrar at any given time to make changes on your behalf.
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