Reliably standing up compute instances, and updating their software, is a core competency. Necessary for any IT environment. But getting servers running is a small component of ensuring a new hosting provider fits into a compliance environment.
New privileged accounts will exist with control over this new infrastructure, who manages those?
Every person needs to be assigned only permissions suitable for their role. Is an identity system change planned?
What networking changes are required to reach this new provider? Can production and QA be entirely segmented from each other?
How are data at rest protected? Depending on your risk profile and paranoia level, you may wish to implement database or file system level encryption. Even if the service provider has evidence that their storage system does disk level encryption.
Secrets, how are they managed? Keys, passphrases, and certificates will exist, so approved tools should be selected.
How do change management procedures work?
What security controls are associated with the infrastructure? Network firewall rules, ideally segmenting QA from production. Multiple auth methods. Resilience of the external facing services to denial of service. Software update compliance and vulnerability scanning.
Hosting providers sometimes make portability difficult by introducing their own special sauce APIs. Any of the above may be relying on features that do not have an obvious replacement at another provider.
What is a worst case scenario if this project fails compliance catastrophically? In the case of PCI, the organization may face large fines, and lose payment processor relationships. Unlikely, but business continuity is all about risk management.
Absolutely this new implementation would need to be audited to achieve the same confidence level. Ideally, improve security and availability over the previous designs.
Designing for a hosting provider switch gives choices, always good for competition. But beware claiming that doing things properly is easy, even for small systems.